Jenn, what kind of early intervention is your son currently receiving? If he's in an ABA program, talk with this teachers and see if they can address this through this IEP.
Will he outgrow it? Hard to know, but if you address it now, you have a better shot than later, I suspect.
My younger son, now almost six, had lots of public tantrums. So we had his home support aide take him out almost every day, with the idea that the more experience he had with unfamiliar situations, the more coping skills he would develop. And since it wasn't we, his parents, who had to deal with these public meltdowns, we were more able (less exhausted and frazzled) when we took him out. I think that it worked, as when we spent June - Dec on the road travelling, he did great, with very few public meltdowns (I can only recall one the entire time - of course, he still had private ones, a few times a week, in fact.)
Good luck. After six years as the mom of two autistic boys, I do think it does get easier.