Should I be worried?

Okay so this morning my boyfriend was sleeping over and his phone went off around 6:30am and I looked over at it to make sure it wasn't for work (he's a heavy sleeper so I have to wake him up) and it was from another girl saying "morning :)" and I'm a pretty jealous person I'd say haha and a worrier so I just don't know if it should be something to be suspicious of? He also kept his phone close after but I don't know if that was just me being oversensitive to it. Like do girls randomly text someone a good morning message if they haven't previously been talking? I trust him but I'm just jealous and a major over thinker haha.