If you need validation from your boyfriend, you need to tell him that. Tell him he needs to be more open about his feelings; he needs to tell you you’re beautiful more often or tell you he loves you more often or whatever would calm you down.
Realistically though (and I know you know this), this isn’t about him, it’s about you. You’re having trouble in your relationship because you apparently don’t believe or realize that you are awesome enough for him to be wholly devoted to you. And truth be told, you are. Especially in a relationship that new, there’s no way he would still be with you if he doubted your adequacy as a girlfriend. You’re great and you need to start believing it and proving it to yourself.
You could start making a list every day of 10 reasons why you’re a great girlfriend (or, hell, a great person). You could tell your boyfriend you’re doing this, and why you’re doing it, and have him help you with your lists sometimes. You could ask your friends what they would put on a list like that about you. You could start writing down every compliment you receive, and reviewing them whenever you feel unworthy. You could exchange weekly love letters. You could look right at the girl he’s talking to and say in your head, “She wishes he liked her as much as he likes me.” You could read about feminist theories which debunk the bullshit idea that women all have to compete for male attention. You could remind yourself that it wouldn’t be the worst thing in the world if you were to be single again because you are fine as fuck and the world would keep on turning.
Self-love and self-acceptance are a journey, and a very personal one at that; you sort of have to seek and find the techniques, resources, and thought patterns that work for you. Journaling is a great way to work through your feelings, figure out why you’re feeling them, and what you can do about them. Try ranting for 5+ pages about your concerns and then making a page-long list of actionable items, things you could do to tangibly improve your situation. Your list might include some of the things I’ve mentioned above, as well as your own ideas.
For further reading, check out these Gala articles: Jealousy is the Killer of Girl Love, “I’m So Jealous!”, and I’m Jealous of Other Women!