Is anyone else possessive over their baby?

I’m a FTM and my daughter is freshly 3 months old. I’ve started to notice I’m very possessive over her. Does anyone else feel this way/have experienced this before? I just hate “sharing” her so badly. I don’t like letting anyone (other than her dad) hold her or play with her. If someone else holds her, I’m screaming “okay give her back now” inside my head. When someone other than me makes her smile it upsets me.. it’s almost like I get jealous or something?? I saw a tiktok of a nicu nurse talking about holding/cuddling the babies; there was a comment of a mom saying she went to see her baby in the nursery and couldn’t find him because the nurses had him at the nurses station.. I would lose my mind if that happened to me, yet the comments were talking about how sweet that is. I feel crazy! I don’t know if it’s related but I am autistic and have always hated sharing anything and everything. Why do I feel this way? Is it normal? I also don’t really want to be shamed for this or told to get over it, just wondering if it’s normal!