Is it possible to contact and have a session with my old psychiatrist again?

You can see your old psychiatrist as much as you want. It's just that you will have to pay her cash out of your own pocket since the medical plan you are on now is different. Tell your mom you need to see her to talk of an old issue she was familiar with. Maybe your mom will agree to pay part of her hourly fee and you can pay the other part. It's worth a try. Good luck.