I never say "don't listen to your doctor", but your PCP isn't a mental health professional and you need to be your own best advocate. Not every Psych works for every person, but there is very, very likely one that works for you who your insurance will cover. Since you have executive function now, it's good that you're taking action now. If you ever run out of executive function, reach out to trusted friends and family.

In an emergency, call 988 if you're in the US or otherwise look up your local mental health crisis hotline now and write the number down.