Am I being selfish?

I don’t know if I am or not haha.

I have a 5 year old son with my ex. We share custody, 50/50. He goes to grandmas to be watched so we don’t exactly pay for baby sitting. I am due with my current bfs baby in Sept so I will be off work until January.

My ex just texted me and told me that since I’ll be off till January, he’s going to sign up for all the overtime he can since I’ll be home to watch him so grandma doesn’t need too. This will also include me driving him to and from school, feeding him, and all that of course. I am not saying I don’t want this but I feel he should still figure out babysitting with him on his days he signs up for overtime. Not that I don’t want to see my son, but the extra days of me bringing him to school, bringing snacks to school, food, gas and all that will add up. Obviously when baby is a bit bigger I would do it no problem but newborns are a lot of work and I’m sure lots of moms have kids and so this everyday.

Am I being selfish by saying no?