There is much written on here about jealousy. I suggest doing a search for it in the search engine and looking at the stickies for some really good threads.
the good news is that you are not alone and it is not uncommon to be jealous... people approach it several ways, but there seems to be a consensus to walk right through it, pull it apart and see what the fear is... usually it is an unmet need, such as enough time together, not enough boundaries set that make a person safe, not enough history together yet, enough attention and trust... that sort of thing, but it can also be that one person is more in love with the other than the other is with them, or that they feel there is some sort of outside threat.
I am not suggesting that any of these fit, but something will and it's a matter of finding it. I would suggest not avoiding it, but sitting in it and really letting yourself feel what it is like to be jealous. I do this alone, and then bounce it all off someone else. That seems to help me. Whatever works for you is the best bet.
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