Dear Reddit, am I being an overly-attached girlfriend?

Hi reddit,

So my boyfriend and I are both almost 18 years old. We've been seeing each other for close to two months, but made it official a little over a week ago. He makes me feel very special and loved, but I have one concern. He has a lot of female friends, which I am completely ok with. Some of which he told me he had romantic pasts with.

Whenever we're together, he is always texting one of these girls. I think it's a little rude that he can't just ignore a text when he's around me, regardless of who it's from....I always turn off my phone or throw it in my purse when we're on dates, just out of respect. It's gotten a little annoying, but not unbearable. I've never snooped through his phone, but I once saw that he texted one of these girls saying "sorry, babe". Babe? Is that something a guy would say to a friend? It kind of worried me a little.

So reddit, is this an issue I should be worried about? Should I confront my boyfriend? Or am I being overprotective? Help!

Thanks.

TL;DR: Boyfriend is always texting other girls when we're together. I read a text where he called one girl "babe". Should I be worried?