Tried other meds, but that side effect is classic for all TCAs (like Nortriptyline). Did your provider start you on the lowest dose? Sometimes titrating up slowly is a way to minimize dry mouth as a side effect.
If you haven’t tried topiramate or propranolol, those are other generic medications that have good preventative migraine properties.
If money is no object or of you have good insurance, qulipta, every other day nurtec or the once a month injectables (ie Aimovig) are the best migraine medications for tolerability and efficacy.
My point is, you should be able to find a medication that works for you, without causing side effects that outweigh the benefit.