Which symptoms exactly, besides nausea, you have hours after playing basketball?
For how long you are experiencing that condition?
Does this subside or it is constantly present?

The main symptom is severe headaches. The headaches start an hour or so after I finish playing and continue for several hours. They gradually diminish after 4 or 5 hours. This happens every time I exercise vigorously. If I eat immediately after working out it's not as bad.

Thank you.

I guess you are experiencing primary exercise headaches that occur most often in young men in their 20s.
One of the reason for this headache can be low blood sugar, as you noticed eating after exercise can make headache less intense. So, you can try a glucose tablete before you begin, and then have a starchy snack or better yet a full meal soon after you finish (within an hour).

Do you suffer from migraine headache, too?
Do you usually see flashing lights before the actual headache?