You're in a pretty tough boat, and I'm sorry for that (though it's great that you have a good relationship starting).

One key that I would focus on is not repressing the anxiety. The more you fight the anxiety, the more it will fight back and the more damage it will do. When you get anxious, find the source of your anxiety and sit in it. Search it out and embrace it. Then, when you're sitting inside of it (mentally), 'hug' the rational conclusions and feelings.

For me it works like this: A new anxiety appears (such as my SO starting a new relationship). At the outset, the novelty is the scariest part. There are so many unknowns to new partners and experiences that your mind goes wild trying to fill them in. When I repress them, I associate pain and suffering with those feelings. The fear of this pain makes me fight more wildly until the worst happens: even the thought of the anxiety or anything surrounding the concept brings on waves of anxiety, fear, loathing, and pain. That's the trap I end up setting for myself.

So, don't let it happen. Sit in the new feelings. It will be scary and it will hurt at the outset, but the more you steep yourself in it, the less novel it will be and the more mundane it will become. The desires in your mind to fill out every possibility (especially the most painful ones) will slowly abate as they seem further and further away and the whole thing starts to become more comfortable. Not completely comfortable though. Twinges of anxiety will still appear, but by then you'll have the tools to combat it easily and a foundation of trust and security with which to wrap yourself.

This is how I deal with anxiety and it's also how I dealt with PTSD. I use the mantra "Sit in it." and focus on the image of the acronym "SIT" (as I'm a bit of a pictorial thinker).

I hope this helps and wish you luck. If you want anyone to talk to, feel free to PM me.