Perhaps it doesn't have to be an either/or. You can begin looking for another counselor while still seeing this one. Continue going to your appointments to get some support and explain your situation: once every two weeks isn't enough for the issues that you have going on and as much as you like her, you need to take care of yourself by finding a T who has weekly (or twice a week) availability. She might also be able to suggest some names. She knows that this is an issue for you and it seems that her schedule will not allow for more sessions/she won't change her schedule to accommodate you, so you need to take care of yourself by finding another solution. All of this is so much easier said than done, particularly when you are in a depression. If this seems overwhelming, is there a friend or family member who could help you to get the ball rolling in looking for another T?

You're doing a great job... keep at it. Safe hugs.