can't stop thinking about someone i cheat with

Do you really want to make your primary relationship work? Then either open that relationship or cut ties with the other person. Your fantasies are your own. But when it becomes real live in-person sex, that's another story.

Make your choice.

i think it is quite normal to fantasies sex with other people. variety is the spice of life leading to this desire. as long as you just fantasies it is not a problem with your current relationship.

Sounds like your not over the affair. You said your not allowed ton see them, why who said

My partner said if we can't control ourselves around eachother, we shouldn't be around eachother. I would like to be open, and my partner did too at one time, but has changed their tune once I started acting on it.

Oh! That information changes everything.

You two once had an "open" relationship, now partner has decided that's not for them and wants you to stop, too.

Open relationships within a marriage (or other relationship) takes a mutual OK. It's now not OK.

You don't say how adamant this partner is with this "rule" placed on you. Is it a deal-breaker for your partner? Have you invited your partner into the relationship, for a 3-some?

See if you can live with what you think is a restriction. If not, separate.. It's not fair to either of you.

Also, consider if this side attraction is a "forbidden fruit" that you are not allowed to have, thus it gets more attention than it really warrants. You may lose something really valuable just for a fleeting fantasy, just based on sex.

For me, you have to choose as early as possible. IMO, you are not very much in love with a person if you still want someone and if you are not contented with the first one.