First, don't assume right off the bat that your son is a she. There's a pretty decent chance it's the case, but there are also boys who are happy being girly boys.
However, it can't be denied that you might have a little trans girl there. The good thing is that he's (well, let's go with he for now because it's confusing and we're not sure yet, shall we?) extraverted enough to make it obvious at such a young age, so you can act now, and avoid at least part of the depression and many other bad effects that could come with puberty.
I think your best course of action is to bring him to a psychologist and the doctor - possibly the very same ones you yourself saw if you trust them - and get his situation evaluated and, if GID seems likely, get hormone puberty blockers as soon as possible.
That's the wisest thing to do when you have a possibly trans child, and what's widely advised. It saves them much of the psychological and, above all, physical effects of puberty, and makes transition, if it happens, much easier. On the other hand, if later on, he decides that he is indeed a he, which happens pretty often if we listen to doctors working in the domain, he can just stop blockers, and puberty will initiate itself normally.
Puberty blockers allow your child the time to take an informed decision, free of the panic and hurry from seeing their whole body changing in an ugly way, and contrary to early HRT and doing nothing, they make both genders viable options when a decision is taken.
They make all the difference, seriously. If there's one important thing you can do for your child, it's that. If he is a he and just goes as a guy, he won't have any problem. Just like many other guys, he'll have a kinda late puberty and won't have the slightest problem with it, normally. But if he's a she, then you'll have saved her all the trouble with body and facial hair and VOICE and muscle and height and bones all the rest of the awful stuff, while allowing her to have a normal ribcage, hips, etc. It's a win-win situation, really.
So while not all doctors are willing to prescribe blockers, if investigating, with a professional or not, shows that it's likely that there's a gender issue, I think you should make finding someone who'll prescribe blockers your number one priority. Because once the physical harm is not a worry anymore, you can focus without worry on the actual issue and make sure.
Also, another very helpful thing is not to put pressure on him either way. Trying to influence him by showing him what a guy is, or by making him do guy's things, that won't help him. The same is true for girl's things. Whatever he is in the end, it's important that he be allowed to be himself, and to determine himself who he is deep down. Second after my body, I think my parents' actions in that regard, in trying to make me a real guy, were what messed me up the most.
Also, while not influencing him, if you suspect there really is a gender issue to be looked into, it might be useful to discuss it deeply, and insist that he thinks about it deeply, too. When I was young, I was asked about it, and because transsexuals were gross in my mind, I didn't allow myself to be one, with disastrous consequences. Now, you child is like ten thousand times more extraverted than I am, but still. Sometimes, people can hide things very well even when they display the rest very readily.
I, for example, was pretty much always kind of girly, but I only once asked for the permission to be a girl, and when I was told no, it was no forever in my mind, and I never mentioned it again until adolescence, in a figurative form, and waited until I was almost an adult to say it out loud again. So while you shouldn't jump to conclusions, it can be a critical mistake to just wait and see how it goes, and disregard something because it's not very persistent in your eyes. I've said it a ton, but that's why I think blockers and psychological investigation are the wisest decision you can make.
