Is it normal for a guy to be "territorial" and protective over his girlfriend?

[Jordan]

My girlfriend hasn't had any relationship before me, and If some guy I know liked her before talks to her, or just any guy she knows starts flirting with her over facebook or whatnot, I tend to feel kind of hurt I guess. It's more of I don't her to talk to the guy because I'm scared of cheating. I also just don'f feel right when anyone is doing something with her, like flirting, holding hands, hugging, etc, even if the person is a professional, if they're discussing something of sexual nature, or say she needs to take some clothes for something like an ecg, I'm very annoyed well in that case if its a male although anything more and I would be offended whether the doctor is male or female. I know the last part is a bit immature, but I have a very hard time trusting people (I trust about 4 people, 2 with everything) and I'm working on that, but it's itching at my head knowing that there's so much I don't know about her still.