Am I overacting?

MIL keeps referring to my son as “our baby”. It annoys the shit out of my fiancé and I and he’s let it be known that (since we have to stay here for HER benefit for some time) she needs to allow us space to be first time parents and not to overstep, not to walk in and just grab him or kiss his face because people’s baby’s are getting sick and some even dying. She says okay but she’s definitely a in one ear and out the other kind of person. For example, a lock had to be installed on our door because knocking and waiting was a hard concept to get. I know she means well and she’s excited but it’s not her baby!