Is it normal to want to be extremely close friends with my ex?

I was with my girlfriend for almost 4 years, and after breaking up mutually we decided to live together as roommates and best friends. We have two cats together and have recently moved to a new state, so we only have a few mutual friends and haven't quite settled in yet. I have so much anxiety about losing the friendship with her that when I go out after work with a friend, I nearly have a panic attack wondering if she'll be upset or weird about it the next day. I've lost 8 lbs in the past month or so after a date I went on caused tension and strain on the friendship. I literally cannot imagine dating anyone new, because I think it would ruin my relationship with her, or would bring a permanent distance between us, and I really don't want that. I know I still love her, but there's no chance we'd get back together, so what do I need to do to have healthy boundaries and to ensure we can both move forward in a way that maintains the friendship? I feel she can be very distant sometimes and is not very emotionally expressive. I feel sometimes that I worry much more about being close friends than she does. Sometimes I feel like I need her in my life, but that she would be ok if I weren't in hers. How can I gain perspective and regain a healthy frame of mind in regard to this?