You look wonderful, I would never make an incision on your eyelids
You are very pretty with lovely eyes and a young-looking face. I definately would not make an incision on your eyelid and try to reduce the orbicularis muscle--you would loose the natural beautiful look of your eyes.
As you get older, if you do consider any procedure at least think about an open fat graft (NOT fat injection!) to plump or fill the depression beneath the bulging muscle. This can camouflage the depression beneatah the muscle and add volume to the area. This also can be done through an incision on the inside of the lid which will preserve your beautiful eyelid shape.
Eye "Bag" Options When Caused by Muscle Hypertrophy
Unfortunately we are our own worst critics.
You have a beautiful face, smile, and believe it or not ,eyes. Sorry that you feel uncomfortable with others looking at you, but as a facial cosmetic surgeon, I will give you my opinion...actually I already have above.
If you were my patient I would treat you most conservatively, beginning with very low dose Botox placed just below your lower lash line. Let that settle for a few weeks and see how you like the result. Once the Botox has had it's affect then evaluate whether injecting Restylane into the lower lid hollows would be indicated.
I would advise against surgery unless you find a highly qualified ophtalmo-plastic surgeon who felt that they could help you (Robert Goldberg, MD at UCLA, Kenneth Steinsapir MD, and Jonathan Hoenig, MD, all in Los Angeles). Even the hands of those experts, surgery should be a last resort.
Now go out there and let all those Texans enjoy your pretty face.
Good luck and be well.
Botox may be worth a try for muscle thickness in the lower lid
The thickness that appears in the photo is not typically thought of as a "bag". Only an exam can confirm, but it appears to be hypertrophy or thicknening of the muscle that lives there.
Botox may, over time, improve the appearance of thickness and achieve your goals. An experienced Botox provider can give you a more precise opinion after a consultation.
Muscle reduction versus muscle weakening
The fullness just below the lash line is generally muscle bulging and hypertrophy. The muscle tends to roll on top of the cartilage plate of the lower eye lid. The methods to deal with this have to do with reducing the volume of muscle with excision or weakening it with Botox.
It would be helpful to see the movement of the muscle as you tightly close you eyes and see the muscle action. The muscle could be weakened with Botox. This has to be done with very small doses to not over do it at any one time. You can add a few more units each week if you need to in order to get the muscle to shrink but still maintain muscle support. Only Botox injectors that are more experienced should do this.
The muscle can also be reduced by excising part of it through a lower eye lid blepharoplasty incision. Again, this should only be done by some one with a lot of lower eye lid surgery experience.
I can tell you are very motivated to get something done, make sure you are comfortable with the experience and expertise of your surgeon.
Possible to perform muscle shaving but not recommended
What you describe is the thickness of your orbicularis muscle. This muscle acts like a 360 degree sling around the eye. It has multiple very important functions: Forcefull eye lid motion, blinking, lid position,tear pump mechanism etc.
This is a natural bulge and not an eye bag and it is better not to try to change it. In very select cases, carefull shaving of the muscle by a plastic surgeon well versed in occuloplastic techniques could be done. I would still not recommend it except if you have real eye bags that you need to deal with in the future. Best of luck!
Muscle hyper trophy of lower eyelids
You do appear to have a ridge of excess muscle underneath your lash line. I have on occasion removed a small strip or orbicularus muscle in patients who required it (these were extreme cases). It require careful judgement as you do need that muscle for proper eyelid function. My preference is to inject a bit of Botox in situations like these in order to allow the muscle to atrophy a bit. The results are subtle. My suggestion would be to take the advice of others here. You have lovely eyes and the ridges underneath your eyelids do not detract from your appearance. I have encountered patients with your situation, and I like to show them
pictures of babies. Lots of babies have lower eyelid ridges, and we certainly don't consider them unattractive.
Better to not have surgery right now
You have a lovely face and I don't think you would benefit from surgery at this time, especially since the modifying the muscles could contribute to an undesirable result.
Lower eyelid bags due to muscle hypertrophy
According to the picture that was presented, yes, indeed, there is a slight hypertrophy of the muscle on the lower lids. It is impossible to go in and remove this because it will leave you with a weakened and paralyzed lower lid and is not advisable to have anything done about it. There does not appear to be any fat pads present underneath the muscle. It does not appear that you are a candidate for a blepharoplasty.
Your eyes are not the problem
In the photo, your eyes look great and I wouldn't do anything based on this photo. I would like to see a photo of your face when you are NOT smiling. Most likely, you have volume loss in your cheeks and under you eyes. This can make you look tired and gaunt even though you don't have any bags under your eyes. The best treatment for this is fat injection to the cheeks and lower eyelid depending on where you need it. This could truly brighten your eyes and whole face.
The fillers are an acceptable alternative to fat injection but the results are not as nice nor are they as long lasting. The other possibility (though less likely) is that you do have fat bulges under your eyes but they are not seen in this photo because you are smiling and tightening your lower eyelid muscles. If this were true (again less likely based on your surgeon's evaluation), surgery would help. I do not recommend trimming or removing any muscle.
Lower Lid Muscle Hypertrophy
I think we all can appreciate the issue that you're having. However, it's not that the muscle is changing but the aging process is changing your lower lid/cheek junction. As we age the deep tissues of the face descend. This creates worsening of the nasolabial folds as well as a more pronounced lid/cheek junction. This junction occurs at the bony orbital rim.
So you have a convexity with the pretarsal muscle (the bulging part) then a depression/concavity down to and just over the orbital rim, then a convexity again over the cheek. So your options have to address camouflaging this concavity.
The least aggressive approach would be dermal fillers along the rim and the inferior part of the lower lid. The next approach I would suggest would be micro fat grafting of the lower lid/rim/tear trough. This would be permanent and fat is youthful so not a bad option. Finally a midface lift to reposition the tissues would be very helpful but is the most aggressive.
Oh, and finally the whole Botoxing of the lid thing will end in disaster. You have thickening of the pretarsal obicularis muscle. This is truly the only area that MUST always be working in order to close the eyes fully. Botox paralyzing of this WILL prevent you from closing your eyes fully for several months. This will necessitate taping your lids closed at night, lubricating drops and months of inconvenience.