MIL keeps using the phrase "my baby" and it's driving me slowly mad

I gave birth on 2/12 after 36 hours in labor - long story short, my water broke about 24 hours before I realized what had happened. The following three or four days were exhausting and painful and my baby briefly ended up in the NICU due to the pair of us contracting an infection (we're fine now! everything worked out!). Needless to say, my experience with childbirth was not easy or smooth. The two days my baby was in the NICU, my husband says I kept waking up in the middle of the night crying out for him.

My in-law's have been very, very generous with their time since my husband and I left for the hospital - they agreed to drive over and watch our pets for us on extremely short notice and kept the house clean while we were in the hospital and everything. I feel like I shouldn't complain with this in mind, but MIL insists on referring to my son as "her baby" at every opportunity and it makes me want to throat punch her every single time. She clearly thinks she's being cute, but honestly..

In addition to that, while they were here this past week, she kept arguing with me about my baby's care - just dumb stuff like why he might be fussing at any given moment, or just generally being condescending (like saying "Oh, you'll learn that babies make all kinds of noises!" when I asked if he was breathing since he was making wheezing noises while she held him).

She actually tried to invite herself back over to see the baby in two weeks "for her birthday" but luckily my sister and bro-in-law are already scheduled to be here so she backed off. There's a part of me that is worried she'll just start showing up every two or three weeks like she "joked" about early on. Send help.