Actually you shouldn't eat ice cream. It's best to avoid ice cream and other milk products for at least two weeks after the surgery. The reason is because milk products generate phlegm, which will cause you to cough or clear your throat and potentially aggravate the healing tissue and increase the chances of bleeding. Just go for foods that are soft and aren't hard to swallow, like mashed potatoes(make sure they're not too thick), tomato soup, or chicken broth.
Your doctor will actually let you know what you should and should not eat. Depending on how much pain you are in. You'll be suggested to eat soups or foods that don't have chunks of anything like smooth ice cream, popsicles or broth. Mostly soft or liquid foods