I don't know how you are defining "personality". Drugs cannot change personality but perhaps you are including energy levels in there (make one a "zombie") or other side effects that would have unintended effects on your sense of how you are.

Meds for depression do not make one "happy" or even "feel better", they can take away the depression so one is at "ground zero" in a sense. It's similar to when you have a headache and take an aspirin and the headache goes away. You don't necessarily feel "good" but you don't have a headache anymore! There's no "attention" on the headache, how you feel physically doesn't take as much of your whole focus anymore.

If I were afraid to take, had questions about psych meds, I would not take them because I would also worry about later compliance. If I had a symptom I did not like, I would stop taking them and that would mean they could not work, whether they might have or not. No matter how helpful they could be, if what is "wrong" with me, what I want the medicine to help, is less of a problem to me than possible med symptoms, I don't take the med?

On the other hand; I think taking psych meds is very similar to taking any other meds. A year ago my medical doctor (I see him every 3 months) said my Vitamin D levels were low. I had read up on Vitamin D and saw that it might help my energy levels, sleep and my asthma so I knew a bit about Vitamin D and when the doctor gave me a prescription for it, I gave it a try, giving it my all. Now I buy my own Vitamin D and take it according to my own schedule. I am not great at how I take it but I haven't seen such a great difference that I feel it is that "important" and I think I see a side effect in myself that I do not particularly like. While one cannot do that with many psych meds, the point is that I tried what my doctor suggested to get first hand, personal usage information for myself and to help me make better decisions in the future.

I would maybe try a low dosage of a med for a significant period, see how I felt, if there were side effects I didn't like, etc. and then make a more informed decision for myself of where to go then? If the side effects aren't too bad, maybe raise that dosage if it is not working well yet or wean off and start again with another med or add a med, etc. I would try not to get too "broad" in my thinking that I got too all-or-nothing in my thinking; I would set a defined time period to try X med (after reading about various and talking to the doctor about what he recommended) and go for it. If it has any side effect at all that you don't like, that isn't worth, to you, its possible benefit with your mental health, then have the doctor taper you off that medicine! I don't take Aleve even though I accidentally bought a huge bottle thinking it was Advil because I tried it and it gives me dry mouth at night and I already have too many problems with my sleep and can take Advil and have it work well.

There are lots of things that benefit mental health, anxiety and depression, and I know you are working hard in therapy to help yourself! It's all about you and what you want!