Always sick 🤒

My BF son is always sick with a cough or fever with runny nose like every week and it gets my BF and I very annoyed because his mother seems to not care . He's gotten me sick plenty of times I have such a weak immune system and being Pregnant doesn't help. Anyways I have mentioned it to my bf like what's going to happen when the newborn baby is here and the other one is sick how is that going to work. Like do I message the mother of the child and ask if she can try to take care of his health a little better since there will be a newborn around ? Any advice on how to go about this ? I know us adults can handle being sick but a newborn I know can't. I have co-workers tell me maybe have his mom keep him until he's feels a little betterÂ