I'm glad you're getting to try the mexiletine. Whenever I post information about the different medication options I always put in a warning about Tegretol. I've known so many people who had depression and even suicidal thoughts on it. It seems to be worse for women than men, so perhaps our hormones intensify the reaction.
This forum isn't nearly as active since the Facebook group started, so you may not get many replies, but if you do a search there were quite a few posts about teens in the group using mexiletine. I think the youngest I've seen is 6 years old. Some took it every day and some just before sporting events. I am not aware of any psychiatric side effects. The main complaint seems to be heartburn so be sure to take it with food or an antacid (which is what the manufacturer recommends).
Did your doctor order a cardiac workup? That's usually done first, monitored fairly closely at first and then once or twice a year after that. It's a good idea to work up slowly. You will develop a bit of a tolerance, but many people have taken it for years with no change in dosage. It's a totally different class of drug than Tegretol. There are still potential side effects, so it's a good idea to be familiar with them by asking for the product insert at the pharmacy.
In the meantime while you're waiting to see the specialist, you might want to try the amino acid L-Taurine. I hear from people who say it is helping them. The dose is 1-2 grams per day (which would be 2-4 capsules). It's very safe and acts like a membrane stabilizer without the side effects. The medical research was done in Italy. You can find it at most health food stores.