Quoting Janetta Kugler:" Respiratory infections, such as bronchitisEar infections (otitis media)Sinus infections (sinusitis)PneumoniaThroat ... [snip!] ... contagious. IMO....its pretty messed up that SO's ex would send(lie about) a sick child to be around an infant that young"
He may have been on the antibiotics for a week already. We don't know. And maybe the ex got it cleared with a doc for the kid to be around an infant. We don't know that either. And maybe OP is an OCD freakazoid and freaks the smurf out so the ex didn't want to mention anything even though he's about to finish the antibiotic.
We don't really "know" much about what's going on or why she lied etc., but chances are if the kid is on antibiotics already, it's probably not contagious.
I wouldn't be letting the kids touch or hold or play with the baby anyway, whether they were sick or not, so I don't really see what the big deal is....
Aside from her lying, but again, we don't know why she did that or what the details are. I don't know how old this kid is, but I used to take doxy for acne and it's an antibiotic. I was never sick. I only took it for acne.