Today brought very rapid improvement on my chord changes!
These were not the best sounding chords, but my fingers were in pretty much the correct spots. What helped (surprisingly) was a tip I saw on two different websites. They recommended strumming at a certain rate, and not waiting for your fretting hand to be ready. Eventually it will speed up to match the other hand. It sounds crazy, but it actually worked.
My fingers were hurting less today, at least for fretting. Anything else that uses my finger tips (like some typing, and unlocking seat belts) still hurts a lot. Maybe some calluses are finally forming?
Overall I am feeling more comfortable picking up the guitar and playing with it. Maybe I'm getting better at this? :)