How does medical separation from basic training work?

Apparently during your son's training they found a medical condition that may preclude him from serving. If the medical folks find the condition makes him incompatible with further service, he will be discharged. The process is thorough and involves not only general practitioners, but specialists in the area they have found the problem. Once he has undergone all the tests, the medical folks will come up with a prognosis and determine his fitness for further service.
You must understand, their decision will be based upon not only his current condition, but whether he can serve in environments where specialists in his problem may not be readily available. If his problem is aggravated by conditions under which he is serving and there is no treatment available, not only his condition is a problem, but caring for him until transportation is available to send him to a treatment center that can properly care for him becomes a priority for persons who would normally be concentrating on other things. There are many conditions that are of little concern to a civilian that can disqualify a person from serving in remote areas.
There is no shame associated with his current circumstance, and as I said, many conditions that are considered routine for a civilian are a potential problem in the military. Don't lose any sleep over it (easy for me to say!), he is being well cared for and will not be forced to do anything that will harm him.
On the other hand, if the medical folks have found it not to be a problem, he may not have had the opportunity to contact you because he is back in the training cycle, or, as young people are prone to do, it's over in his mind and he doesn't realize you are home worrying about him. If that is the case, you have my permission to render some corporal punishment at your earliest opportunity.

I was able to call the battalion number that was on their Facebook page. I didn’t get a lot of information other that it can take a long time for the process with multiple trips to see the doc and the med board may not even grant it. That’s why I’m wondering it he’s still training in case that happens. All I’d really like is a phone call from home to let me know what’s going on so I know what to do with the reservation I made for his graduation.

If your son has already been informed that he’s being medically discharges, he will not continue to train. He will most likely stay with his unit until he’s processed out but will do barracks watch and other details within the limits of his profile. I’m surprised that it’s been two weeks and you haven’t heard from him. You might want to contact his units first sergeant for more information. The discharge would be under the Trainee Discharge Program (TDP) if they still call it that. If he’s been told by medical than it shouldn’t take more than a month for the entire process. However that was how it worked when I was a drill.