Lower lid blepharoplasty is your best bet
Many thanks for your photograph. It appears that you have some herniation in the lower lid orbital fat pad that now gives you puffiness below your eye. Typically this is worse when you look up as in your picture. It does not appear that you have skin looseness in the lower lid. My suggestion would be to consider a trans conjunctival lower lid blepharoplasty and also consider adding some fat grafting in the cheek just at the orbital rim. Many people and fat here as a way to improve the tear trough or gutter just below the fat pad. Always consider the advice of it always consider the advice of a board-certified plastic surgeon or a oculoplastic surgeon for this type of case. Find a doctor who does more than 100 per year. Many thanks and good luck
It is important to see an eye doctor (ophthalmologist) to ensure general eye health.
After that you have two options, filler injection under the eye or lower eyelid blepharoplasty.
The bulge under the eye is excess fat that can be removed surgically to flatten the skin.
The puff under you right eye is most likely fat. It can be prominent because of herniation or because fat around the bag has atrophied. The improvement can be simple Juvederm in the under surface of the pad to smooth and fill in the valley. The juvederm is placed on the orbital bone usually. This is temporary but likely will last a year. The other possibility is surgery to correct the area. If surgery is done, it is usually best to not simply remove the fat because this may leave you with a hollow area. Placing the fat pad in a deficient area and wisely using the fat is a definite possibility. My Best, Dr C
Under eye puffiness on one side
While it is unusual to have puffiness on just one side, this can occur. You need to be seen in person to see if anything else might be going on. If everything else is fine, you can certainly improve the appearance with either fillers or surgery.
The lower eyelid bag is not a sinus issue.
Surprisingly there are many causes of lower eyelid bags. This means without an actual physical exam which would immediately ascertain the cause of this contour issue, it is not possible to know what underlies this particular contour problem and, by extension, what the best solution will be. Rest assured though, it can be helped.
First let's recognize that in your photos you are looking up. This will always make lower eyelid contour issues look their absolute worst. Put your finger on the top of the bulge. If it is hard, you are feeling the orbital rim. Generally these are best helped by filling the hollow under the bulge. If the bulge is soft, it may very well be orbital fat, these are best addressed with an arcus marginalis release surgery.
Look for a well qualified eyelid surgeon to assess your issue and remember that the best treatment for this may not be surgical.
Without examining you and knowing more about your medical history, I cannot tell you what might be causing the puffiness under your right eye. If there is no medical issue involved, it is most likely due to some herniated fat under that eye. Treatment options would include injecting a filler, such as a hyaluronic acid filler, under the bag to help camouflage it or to have surgery to deal with the fat. Surgery would be a more long term solution that the filler.
Right sided puffy lower eyelids
I recommend you be fully evaluated by an oculoplastic surgeon. Have you had your thyroid checked? Don't just jump into surgery. Once fully evaluated you can think about different surgical options.
Let us know if you have any questions. You can learn more about lower eyelid surgery from the link below