The weather is cool and the baby burps.
If it's not canine distemper, it's just a simple upper respiratory infection (commonly known as a cold), so take good care of it. The cause of the cold is the decline of self-resistance, not any infectious bacteria. Considering that the weather has turned cold recently, dogs also like to climb the stairs to sleep. This should be noted.
You can consider dressing your dog. Feed some vitamin c in addition. If you have licorice slices, you can also consider giving them. Of course, if you still don't get better after 3 or 4 days, you must see a doctor, otherwise it will cause bronchitis and pneumonia.
As for bathing, I am mainly worried that the dog's resistance will drop, and it will get sick if it is not dried in time after bathing. If the landlord can guarantee to dry it immediately, you can actually take a bath. If it is really dirty, the landlord can consider using dry cleaning powder to let him take a bath.
As for burping. . There is no good way for people to burp. . . Let alone a dog. . .