Sorry you got the runaround! Of course it is safe to give your dog the Trifexis, even though it is 10 days late. Some people give their heartworm preventatives every 45 days. This is no longer recommended because the heartworm cure manufacturer is having difficulty keeping up with demand so it is safer to stick with the 30 day protocol now. But if you do your research on the lifecycle of the heartworm you will see for yourself that being 10 days late one time is not going to lead to a crisis.
As long as you wipe him off, he should be fine. If he shows any signs of an ear infection, take him to a vet and they will most likely prescribe him some ear drops or something similar