What can I do for hooded eyes I was born with? (Photos)

Your photos indicate that you have very full eyebrows which , in conjunction with the upper eyelids contribute to  a hooded appearance. Your eyelid margins are at a normal level,however, and you should not be experiencing any visual obstruction from them. It is unlikely that this is contributing to your headaches, however, you should see a specialist such as a neurologist to evaluate what may be causing them. Any surgery on your eyelids would be considered cosmetic in nature and not covered by insurance.

For significant improvement, hooded eyelids require surgery if there is enough skin. For nonsurgical treatments: Radiofrequency (Thermage or Venus Legacy/Viva), injectable fillers, and a Botox brow lift can help contour the eyebrows and lift the eyelid skin. I recommend getting a formal evaluation with an experienced cosmetic dermatologist. Best, Dr. Emer.

This is a common question. Upper eyelid hooding can be corrected with blepharoplasty or cosmetic eyelid surgery. It is one of the first cosmetic surgeries people usually get. While the average age might be 30 to 50's, some patients get this done in their 20s. It really depends on your unique anatomy as well as what exactly is bothering you. 
I understand your hesitation with wanting to get cosmetic surgery done. Botox injections as well as laser treatments can also be a tremendous benefit if you are not interested in surgery. Of course, there are also many combinations.
The recovery & downtime is very minimal. There are usually no drains, most people can go out the same day, you can shower the next day and most patients take no pain medicine. There are never any guarantees of course with any procedure whether it is surgical or nonsurgical in nature. 
I would recommend that you see a board-certified plastic surgeon in your area that is a member of both ASPS & ASAPS and performs a lot of eyelid lifts but also offers all the nonsurgical options such as injectables and laser treatments. Go over your concerns with them and make sure above all, you walk out of there with several options and an idea of the pros and cons to each of them as well as realistic expectations. 
I hope this helps answer your question. If it does, please take a moment to up vote this answer on the “respond” button on the top right.  

If it does bother you, conservative upper blepharoplasty (skin removal) can be beneficial. Consultation is needed if they are bothersome.

Thank you for the question and the photographs. Having hooded eyes as such will not cause you severe headaches but if you do have a lot of lateral hooding and extra skin above your eyelids, you are probably constantly strainign to have your eyes fully open and are inadvertantly causing more pressure on your eyelids. This can cause eye strain and headaches which a number of my patients do complain about. I suggest you see a plastic surgeon to assess you. In terms of cosmetic versus functional - with blepharoplasty, you remove any skin that is non functional so this will definitely help with what you are describing. I have operated on a number of younger patients who do have the skin excess that makes their eyelids heavy/ they look and feel constantly tired and have very similar symptoms to what you describe. The upper blepharoplasty works very well in these cases. I hope this of help to youBW