Are these signs of teething?

So since yesterday, my son has been sleeping awful, has a stubborn butt rash, which he almost never gets, nothing new was introduced into his diet..and he's very crabby. He was very irritable a bit ago, which isn't like him..and was rubbing a toy on his gums. I decided to check for signs of a tooth but didn't see anything. After I rubbed his bottom gum, he cried..as if he was in pain. He hasn't hurt himself and from what I can tell he is not coming down sick. Is he teething? Can babies be irritable from teething pain even when you can't see a tooth under the gums?