Carolyn, I would suggest starting with a regular throat swab to check for strep...you can go from there, depending on what it shows

If the cough improved on the antibitotic that would indicate to me that a microbe may be at the root of it
Whenever there is an up in tics coupled with a sore throat...I tend to wonder about strep

I am not suggesting you may be showing PANDAS....just that you may have a strep infection at the root of all this
If so................you know what many have learned....that zithromax/azithromycin seems to be more effective than the penicillins or cephalosporins