Maybe Fifth's Disease which is harmless unless you are pregnant. It's also called "slapped baby" disease because the cheeks can get real red like the baby has been slapped. It's a rash that comes up on your stomach, arms, cheeks and can come and go for a few days. It is a relative of measles but like I said, harmless for most- just stay away from pregnant moms because it can cause miscarriage if a pregnant mom is exposed to it. Usually adults don't get it because they have it as kids-but I have had it four times as an adult so it is possible! Adults tend to have joint pain, also.
It could also be heat rash but because you had it and then the next day your son had it, that makes me think of something contagious.
If it doesn't go away, I'd check with the doctor since your baby is so young. Tiny babies do get lots of rashes for no reason but it would make you feel better I'm sure to rule out anything else.
Good luck!