Overheating

My vehicle listed above was doing fine. All of a sudden, I noticed it started running hot, while sitting in drive thru. I put it in neutral and gave it some gas, but it continued to run hot. Temperature gauge pegged out as far as it could go. When I finally got going, it would not cool down, like most cars do when running hot. I stopped and shut it off. Let it set about an hour or so and cranked it back up. Temperature gauge was sitting where it runs at normal temperature. Drove it 2 miles down the road, to get it home, and it was running little over half way. Didn't notice the first time, but did notice the second time, after shutting it off. The fan did not come on. But if it was the fan not working. Why would it not cool down going down the road? And when it pegged out on temperature gauge, it was not boiling smoke from under the hood. It's full of water. Help! Please.