Yes, multiple antidepressants can be a handful, but assuming your doc is a psychiatrist who understands this and can handle it well, it'll be fine.
(Had a bad experience with a GP trying to get me on antidepressants for anxiety even after strenuous arguing that I am bipolar, on meds for bipolar, and just need something for occasional anxiety.)

From what I can tell after some reading up, Elavil can be quite effective as a medication treating trichotillomania.

It is sort of off-label, but if you think about it, hair pulling is a branch of anxiety disorders, which are often treated with antidepressants.

Just be aware of side effects and contact your doctor if there are any that are alarming or just make you feel uneasy about it.

Also, I would suggest CBT with a therapist, if you aren't already seeing one.