Sick Baby

So my 5 month old started daycare on Monday Sept 19th. & that Thursday Sept 22nd he got sick. It got worse over the weekend so we took him to the doctors & they said that he has bronchitis, & said it's possible that he may have asthma, so they said to keep cleaning his nose & give him Tylenol for his fever. So we did that & he started getting better until Tuesday he caught a fever out of nowhere & then he got better. & now he's coughing like crazy out of nowhere & im starting to think that maybe it is asthma & ready to take him to the hospital. He has no wheezing that I can hear from his chest but that doesn't mean that they wouldn't be able to hear it from their stethoscope. & he still has been going back to the daycare since.