Some people will tell you he's too young, but I think you should trust your gut. My kid got his first tooth at 4 months, and then nothing for many more months.
Definitely rotate the teething rings so there's always a cold one in the freezer. They don't stay cold for long once they're out. That's why he cries again after a little while. Some people use a wet & frozen washcloth too but keep an eye on him.
The baby Anbesol wears off too. So does the whiskey. Some people say vodka too. I didn't give my kid alcohol, no matter what my mother-in-law said.
And do call the pediatrician any time you have a question like this - they take calls all the time from new moms. It's not an emergency so don't call at 3 AM, but do call anytime during regular hours and someone will surely call you back later that day.
Good luck! By the time you get this figured out, he'll be on to something new! Ah, the challenges of parenting! We all support you though!