That sounds terribly similar to my experience after DS's birth. I had no headaches during the pregnancy, but a few days after his delivery, they set in BIG time and basically left me unable to function on even a basic level. I was discharged on my final release with percocet for the headaches (CT ruled out anything super bad) and followed up with my new internist for both lingering bp issues and headaches. The headaches continued after my bps normalized and we initially tried to treat them with drugs like imitrex. Eventually, given the absurd number of headaches I was having (pain, auras, nausea, vomiting, dizziness), we decided to try inderal (propranolol) which is used to treat bps, but is also used to *prevent* migraines as it's a maintenance med. This is eventually what did the trick for me. Oddly, I had a lot of headaches throughout DD's pregnancy, but haven't had any migraines since. Strange.
Also, I wanted to ask if you by any chance had a c-section with a spinal? If so, you could be experiencing a spinal headache. Does the pain stop when you lie completely flat on your back? If so, it could be a spinal headache which can be fixed by a quick blood patch.
I hope you were able to get some thoughts from your primary! It's horrible when preeclampsia just keeps messing with your life and well-being.