Not sure if this feeling is normal or will ever go away

I’m 37 weeks and my boyfriend has another child from a past relationship. She’s the cutest thing ever and I genuinely love spending time with her. This weekend my boyfriend and I were putting some furniture because we just moved in together and I noticed myself getting a bit territorial. His daughter was trying to open the various boxes we had that contained her siblings toys, bottles, clothes, etc. And calling them hers and when asked to put the things back or not to open them because they weren’t hers, she would start crying and throwing a fit. I started having thoughts like “those are for the baby” and overall I was feeling sorta protective over the baby’s stuff. Then I was laying in the bed with my boyfriend and she comes in and I thought she wanted to cuddle with us so I made some room for her on the bed and she started to push me off and would cry if my boyfriend said anything to her. I believe she knows that there’s going to be a huge change soon and I understand she just wants to enjoy as much time with her dad as possible before the baby comes into the picture. I just can’t help but feel protective over my child’s things and over my space. Is it normal to feel this way? Is it ever going to go away? When I catch myself having those types of thoughts, I immediately feel guilty...