To answer your original question - no, you don't need to "reset" your count.
That likely is a phrase you may see with caregivers whose kitties are on the depot insulins like Lantus, Levemir (or biosimilars), who are following the TR dosing method. To my knowledge, that doesn't exist with Vetsulin because it is an in and out insulin, so fur shots wouldn't affect your curve data unless of course you did a fur shot the day you were running a curve. Running a curve gives you a snapshot of you when your cat onsets, nadirs and how much duration you are getting that day, and is helpful when making dose decisions. That said, you have plenty of data, and multiple tests each day and night, so running a curve on any particular day likely won't give you much extra info on how the insulin is working for your cat (since you are basically catching lots of data daily anyway).