I'm not sure why the doc would say no- it's absolutely possible he is teething at this age. Did the dr say what else it COULD be? That just doesn't sound very helpful.
My son never chewed on anything- I don't know why. He would be completely miserable but wouldn't chew. A friend of mine would give her daughter a leather strap that someone had given her who worked with leather. It was really long and large enough not to be a choking hazard and it wasn't dyed or treated with anything, and she swore by it. My mom swears by the cold or frozen washcloth. I can't vouch for anything personally.
One thing my dr told me was that the Orajel stuff will actually make their gums tougher and thicker if you use it a lot, so teething is actually more difficult and takes longer. I just wanted to warn you about that.
As for the Melaleuca Oil, I love that stuff. But NO WAY would I have put it in my baby's mouth. It isn't meant to be swallowed, and it is really strong tasting. I have gargled with it when I had a really bad sore throat and it almost made me throw up, and that was like 2 drops in a cup full of water. Always ask your doctor before you give your baby anything, natural or not. Lots of things are natural, but if you aren't a hundred percent sure of what they are supposed to be used for or how safe they are, you shouldn't give them to an infant.