Hello Becca, you are a very sweet LOOKING baby girl! I put looking like that because mom is telling tales on you -- ALREADY, ha ha haaa!

Reverse sneezing is not usually a concern; bichons do it often.

The cough I would discuss with the vet. Did you have a wellness check with the vet when you first got her?

Kennel cough, you would KNOW that, it is a horrible deep cough and keeps the entire home awake at night. No matter she is a small dog; you would know the sound, even never having heard it before.

I'm not sure if Becca would qualify as a "Brachycephalic" dog. Pugs and Pekes are. A few bichons are. The muzzle / nose is very short, and the head more flat. Makes for breathing issues. Cough is one of the signs. Read up a bit on it, and ask the vet about that, too.