Glad to hear Teddy's doing better... and, yes, it is coincidental and one really doesn't know if the meds worked or if the cough cleared on it's on... that's why it's important to finish the meds, bc if they are stopped and it was a bacteria, it could return and become resistant to the medication.
It does take time to establish a good relationship with a vet. I think it's also important to know some basic Yorkie info, as Yorkies (and small breeds) need more specialized treatment than larger dogs. There are articles in the YT Library that have specific info on different topics, such as vaccine and anesthesia protocols, emergency situations and more that Yorkies owners should be aware of and become familiar with.
It's sounds like you're being a very good Yorkie Mom. We're all here anytime you have any questions or concerns about your baby, (or anything else too) and I believe with Yorkies, it's always better to be overly cautious than not concerned enough!