Sharing Our Innermost Thoughts

My boyfriend’s best friend is a girl. She’s also my ex, we dated for like… two-three weeks? They’re really close, I get that. They’re best friends after all. But sometimes they’re too close. When me and the girl were dating, our friends saw him with his arm around her or like… whispering in her ear. I thought one of my friends was just saying that to randomly throw me off, but everyone else in our group agreed they’ve seen it too. He would always quickly remove his arm or move away from her whenever I entered the room. Now me and the boy are dating and everything is going well… but sometimes when they’re together, they get close, extremely close. I won’t know where he is sometimes and he’ll just come from the stairwell or classroom at school with her and they’re playing some type of tag game that requires them to sort of hold each other.
He doesn’t hold my hand in public for long. He’ll hold me, hug me, even kiss me in public, but for some reason, he won’t hold my hand. Especially when she’s around. He’ll actually forcibly and quickly move his hand from mine when she walks over.
Things between me and him are going great. I really love him and he’s always finding ways to tell or show me he loves me. But when she’s around, he’ll change sometimes. She’s a very beautiful girl, everyone in school thinks so. She’s quiet and nice, too. But she doesn’t hang out with a lot of people. Maybe I’m just insecure, but this for some reason is bothering me so much and I don’t know what to do. Is this normal behavior? I’ve only ever been in a commited relationship once before and he didn’t act any differently around any friends. Maybe it’s just my current boyfriend’s personality?