My puppy has fleas, get short hair?

So my 16 week old american eskimo puppy had fleas and we went to the vet to get it some gel to put on their neck and the groomers to get a medicated bath and a trim. But he still has been itchy. My mom wants to get him to the groomers again and cut it really short this time so its easier for us to spot and get rid of the rest of the fleas. We went 3 days ago... should we go again and cut it short? And will the gel thing wash off? And i'm pretty sure he hates it because he was crying last time we went.....