Hi lion, I wanted to tell you welcome to healing well forum. We are happy to have you. I was on Tegretol a few years ago for seizures due to my MS. I had some hair loss when I was taking it, more during the first month or so then it tapered off to just losing a few strands in the shower or when brushing it.
With those medications and you stating that you feel like you are not seeing an improvement in the last month of taking them...it will usually take months (depending on med) to reach therapeutic level in your body for you to notice a difference. Some it is 4-6 weeks for antidepressants and tegretol I think is like 6-8 weeks, so please hang in there with your prescribed medication regime. I hope things get better for you real soon. Take care