Oh, Jersey!! I don't think they Lysol product you mentioned has bleach, but if it did, yes... don't mix that with anything, although the danger there is chlorine gas.

It's probably the acid in bar keeper's friend. Unfortunately all you can do is rinse it, like you did, and dress it like a burn.

Lucky for you, acid burns like yours are probably the best chemical damage you can sustain. The damage should be pretty local and if you take care of the wound you should be ok. I don't think anything you used is going to cause any systemic or long-term damage. You can call the Poison Control Center for more advice, though, from people who know way more than probably most of us do.

Take care of yourself! I'm so sorry that this kind of highlights the difficult situation you're in now, with medical coverage and H's job and everything.