Dealing with relationship anxiety?

I'm in a relationship with my boyfriend for just about two months. I've only had a serious relationship once before, but it only lasted for about five months, and after three months the love was basically already vanishing.
I don't fall in love easily, but damn, I love my guy so much... I've never felt like that before and definitely don't want to lose him.

However, I'm also struggling to keep up. I have struggled with bad anxiety when I was younger. Mainly fear for rejection, anger and loss of the ones I love and care about. Those were always my parents and few friends, cause they were my rocks, my lifelines, but now THEIR ties are so secure and strong, I haven't felt real anxiety for years. I thought I was over it. But now I have someone else in my life, someone new, I suddenly experience a flare-up of anxiety and irrational fears.

I'm so afraid to upset him or lose him, even though I know he loves me more than anyone and I can depend on him fully, and have a hard time dealing with him being away/not chatting/talking for even a few hours, even though I desperately want to retain my own personal space too. I'm so afraid to do wrong things and make him feel like I don't want him or am ignoring him (he's a bit insecure himself too). In my heart I know our love is stronger than any of those things, but my mind just over analyses and makes every little thing or frustration on his side a huge matter.
This is both extremely taxing on MY body and stress levels, and I figure, also on his.

Anyone has advice on how to deal with this? I don't want to give up on him or love. I know it might sound idiotic and desperate, but if I give up now... I don't think I'll easily love again. Not saying it will never happen. I never say never. But since most of this feeling springs from within me and I doubt I'll ever find someone I love as much as him, I would just rather settle on being alone than get hurt again.