Should i see a specialist for drooping eyelid, or can my regular doctor take care of it?

Depends: If both eyes are drooping or one droops over a short time frame, there could be some pathologic event causing this and you should see your ophthalmologist. If both are drooping because of older age heaviness of the upper lids and brow, this is probably cosmetic and you can decide if you want it corrected.

Oculoplastic surgeon: See a qualified eyelid surgeon, who can determine the cause of the drooping eyelid and give you all your options, including observation, surgery, or a referral to a medical specialist.