Should I be worried about this cut? / How common is infection from handling raw meat?

Butchers who handle meat commonly are a trisk for brucellosis and such, From a single incident, I would guess your chance of infection from a wound that bled a lot and had topical Bacitracin applied is about 1%. I wouldn’t lose sleep unless things change.

Can you ger botulism from an open wound? Other clostridia species can, so the answer is probably yes. But for a frozen patty, I would suspect this ain’t that common. Which kills my party idea of rubbing canned chicken over my festering coldsores.