Is it normal that i'm super possesive of my bff?

Ok well my best friend is amazing. She's the prettiest girl at school and I absolutly love her. We do literally EVERYTHING together. Sometimes I even feel like I know her better than my own family... She's like a sister to me. But so we have other friends too, and sometimes I go off with another friend, and sometimes she does too. When this happens I feel like that person doesn't know her at all and wha is she doing with her?? And does my bff feel like this when I'm with other people? Idk maybe I'm weird but I feel like I'm jealous or something? But why should I be... Like she's my best friend and we are completely inseperable. So tell me, IIN??