I noticed my infant was tongue-tied a couple of weeks after her birth. (It generally runs in families. My brother had his snipped when he was a couple of years old.) It was probably causing nursing issues, although we had kind of figured out a way around it by then. Still, I asked my pediatrician about it. (They don't even look for this condition anymore.) She referred me to a specialist who agreed with my diagnosis. She snipped it there and then, no anesthesia, just a little bit of sugary substance beforehand followed by nursing afterward. It was easy, and my dd has much better use of her tongue and, according to the specialist, snipping it probably loosened up the muscles in her jaw.
I'm not sure how this procedure would go for a 3 yo. Depending on the severity, they may very well not recommend snipping it. You probably want to see a specialist. We saw Mary Ann O'Hara in north Seattle. It might be worth a call, at the least.