Dating after Divorce

I got divorced in January of this year and just started dating again in September. My boyfriend now is really awesome and we've hung out everyday for the past couple months (end of august to now) but to be honest I don't think I'm fair to him sometimes. I care about him a lot but sometimes I'm snappy and hateful over dumb stuff and I think it's because I'm kind of afraid to get close again. I know I should just enjoy our time together but sometimes I can't help but get worried that he'll go on about his way and I'm already used to being with him everyday. I get snappy as defense to sad/worried I guess if you get what I'm saying... P.S my ex husband cheated on me with a 16 year old girl that was our neighbor so I think it's normal for me to feel this way I just wish I could deal with it a little better and not take things out on him.