+10 POINTS**Does this sound like my boyfriend has a jealousy problem ?

You sound very young. If you aren't hiding something from him you shouldn't be telling him the conversations you are having with other men are private or "secrets". Sounds a little bit like you are leading him to believe you have something going on with another guy by doing so. That's probably why he is so interested and feels the need to check your texts. He needs that assurance you aren't cheating.