Does the dentist always give you nitrous oxide when getting a tooth removed?

No, every dentist does not give nitrous oxide. Usually only "oral surgeons" use it. Nitrous oxide is usually only given during major oral surgery and having one extraction is not "major" oral surgery. They will numb you just as they did during your root canal. It is uncomfortable but no more than the root canal. You can try and find an oral surgeon to remove your tooth that offers nitrous oxide if you are that concerned about it. However, be aware that many times insurance will not cover it because they deem it as unnecessary for such a simple procedure so you may have to pay for the nitrous out of pocket.