I had bad headaches for 3 weeks after cortisone injections. is this normal?

No: That is not a typical reaction to a cortisone injection. Assuming this was no a spinal injection (which is a different topic altogether) i would look at other things that the cortisone could have done. One common is a rise in blood sugars. If you are prone to higher blood sugars, this can cause a rise that can make you ill - headaches, fatigue, urinating more, etc. Ask your dr to check...

If it is an epidural: If this was an epidural steroid injection, there is a 2% risk of what is called a spinsl headache due to an incidental puncture of the dural sac leading to a small leak of cerebral spinal fluid that usually resolves on its own but occasionally requires an injection of your own blood at the original site of the epidural iinjection which is known as a "blood patch." this seals the leak.