Is it worth a trip to the doctor for drooping eyelid?

Yes. Any change from normal should be evaluated. Causes of drooping eyelid can include underdeveloped lid muscles, trauma, nerve or muscle damage, or even tumors or stroke-type conditions, to name a few. Knowing the cause of the droop (or at least ruling out the more serious causes) will go a long way to comforting you and providing treatment options.
Droopy eyelid. There are several causes of a droopy eyelid. Your best bet would be to have your eyes evaluated by a board certified facial plastic surgeon.
Depends. If your eye droop is of recent onset, it may reflect some neurologic issue such as a vascular change or tumor. Especially so if accompanied by a change in eye position. If gradual it might be a muscular problem or myaesthenia. Your ophthalmologist can sort this out and provide what relief is available.