My teenager seems to have diarrhea, vomiting, stomach pains, and headaches frequently.?

first take him to a doctor to have a thorough check done on physical reasons. if that comes back fine then it is an emotional issue and you will have to look into bullying etc.

Have you been to a doctor? Have you tested your water? If you can't afford a doctor, and your state government made a coverage hole for affordable health care, find a clinic or the county health department.
If you can't find affordable help, when you see a doctor, ask them how much medicare would pay them for something. Doctors and hospitals have to inflate their prices in order for insurance companies to say they're getting their customers a deal. The amount medicare pays them is a lot closer to reasonable, and most doctors will accept that amount.

edit:
Get an opaque bucket with a lid. If he's having diarrhea frequently, it shouldn't be too difficult to get a stool sample. The lid should make it a little less humiliating.

and you haven't taken him too a doctor?

Take him to the doctor or hospital. He is obviously dying