Insecurity in relationships?

Ok, to make a long story short, I was home-schooled and was pretty much isolated so never made any friends. Now to the present:

My boyfriend and I have been together for almost a year, he's great. He tells me that he thinks I'm beautiful all the time, tells me how much he loves me and wants me, etc.

The problem is I'm so insecure all the time no matter what! When we first got together I didn't really think much of whether the relatioship would last or not, it either would or wouldn't. But as times gone past I've started getting ridiculously insecure & jealous if he even mentions another girl (for example: a few girls grom uni had invited him to come over and play board games and chill out, I started giving him the silent treatment and then when he asked what was wrong I exploded at him, even though he had asked if I wanted to go with him!!) Another girl I knew he had made out with before we got together sent him a message on facebook saying she missed him and I burst into tears! A few months ago I even checked the messages on his phone (which he found out that I did) and even then basically said I could check it whenever I wanted, he even gave me his facebook password! He trusts me completely with all these things and he has never left any doubt in my mind that he only wants me. And yet I still can't seem to get over it and it's starting to become a daily argument. He say's it makes him feel like I don't trust him and that I think he's gonna run off or jump into bed with the first girl that comes along. I've also been dx with a chronic illness not long after we got together and he has been there for all the really hard times. To me it's like why would he want me when I'm sick most of the time?

My main question is how to overcome insecurity?

Especially when your partner never gives you any reason to doubt?

Thanks in advance