You shouldn't blame yourself for the reaction your parents had to the ice cream. I don't know all the details, but it sounds like there was some over reaction. I'm sure your parents don't hate you. It was merely a misunderstanding that seemed to get a little out of hand.
I've gotten into arguments with my family too. It's no fun. Some times, you have to learn to let things go. Some battles aren't worth fighting. You really do have to walk away from some situations. The grief isn't worth it.
Try not to worry. I'm sure this will all blow over before you know it and your parents will be upset when you leave to return to school. You may be an adult now, but to your parents, you're still their baby. They do worry about you even if it doesn't seem like it some days.