Without at least a photograph, it is impossible to make an intelligent response
It certainly sounds like you have an issue. It is thought that rubbing the eyelids can have a long term effect on the eyelid architecture. There is good evidence that this type of chronic eyelid rubbing can contribute to changes in the cornea that cause long term thinning of the cornea and in some cases a condition known as keratoconus.
As mentioned by some of the responders to your question, prominent eyes also suggest a condition of Grave's eye disease. Do you have this? From the description you have provided, it is impossible to know. Another condition that can cause significant wear and tear on the eyelids is obstructive sleep apnea.
My recommendation is to consult with an oculoplastic surgeon. This is a board certified ophthalmologist who has gone on to complete specialized fellowship training in eyelid, orbital and facial surgery. Ophthalmic Plastic and Reconstructive Surgery is one of only two plastic surgery specialties recognized by the ACGME, the American Council for Graduate Medical Education. The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains a website with a directory to assist you in finding a well qualified oculoplastic surgeon near you: ASOPRS.org.
Treatment of puffy eyelids
It sounds as though you may have Grave's disease. It might be worth checking with your primary care physician or local endocrinologist to test you for this. Otherwise, you may need a combination of eyelid surgery and surgery around the actual globe of the eye to correct the problems that you are encountering. Make sure you get several opions, and visit plastic surgeons as well as some oculoplastic surgeons to see what options you have and to see what you feel the most comfortable with. Good luck!
Patients with allergies do tend to get bags much earlier than other patients. Sometimes surgery is the best option. If you are not ready for surgery I sometimes use Restylane to disguise the bags and fill in the valleys along the lower lid and side of eyes. Botox or Dysport can be used to lift the brows and sometimes minimize the excess skin in the upper lids and brow area. The bulging should be measured and evaluated. Sometimes a medical condition such as thyroid disease could be the culprit.
Treatment options for puffy eyelids and bulging eyes
It is important to get your allergies under control through allergy testing, desensitization shots if needed, and cortisone nasal sprays and antihistamines. Once allergies have been addressed and taken care of, make sure that you are not eating a high-salt diet and getting fluid retention in the fat pads on the eyelids. Bulging eyes could be a thyroid issue and need to have your family physician address that to make sure that you do not have thyroid disease. If all the above has been corrected, a lower transconjunctival blepharoplasty can be performed. This is done under a general anesthesia that takes approximately 30 minutes, you will have bruising and swelling that will last approximately two weeks after the procedure.
Puffy Eyes Needs More Than Surgery
The puffy eyes can be a symptom of an underlying medical condition related to thyroid, allergic condition, kidney disease etc. It needs to be throughly evaluated by an internist. Once it has been established that you do not have any serious underlying medical condition then you can undergo a conservative blepharoplasty to reduce excess fat and skin.
Allergies won't cause bulging eyes or eyelids.
Recurrent bouts of swelling of the eyelids at a young age that leads to permanent effects may represent a condition known as blepharochalasis, which is quite different than the age-related changes of the eyelids. By your description, allergies alone would not do this.
As for the bulging eyes, it would be very important to determine whether Graves' ophthalmopathy is present. Graves' disease is a serious thyroid condition that can also affect the muscles around the eyes.
An appointment with a good board-certified ophthalmologist might allow for an accurate diagnosis. Treatment of the bulging eyes from Graves' disease has several options, but orbital decompression often works well, followed by correction of any resulting double-vision. And endocrinologist or internist can help with the thyroid issues.
All the best,