I'm uncertain why Baytril would have been given for a nondescript sinus problem. More often than not, it's simply dry or inflammed skin/mucous membranes pending a shed or resultant from a previous problem. The mucous expelled from the nostril leads towards more of an infectious problem; perhaps this was seen by the vet as well (?)

To answer your question; if the problem is going to be solved by the Baytril (ie, your husbandry is fine and the cause was a Baytril susceptable infection) then you should see noticeable improvement in the first week. Probably in the first few days. Still continue the prescription until finished. If no improvement after the first week, call the vet for further advice but don't stop the Baytril until told to do so.

Ian