Well, it can't be good. I found news articles where nurses accidentally injected breast milk into a babies IV.
“It’s not meant to be in that place,” he said. “What happens is that it goes toward the organs and starts clogging them up. It doesn’t flow through the very tiny blood vessels…. It starts clogging the lungs up or it goes to your brain, or whatever other organs.”
You are much bigger than an infant, so maybe you will be alright. I imagine that milk would curdle and chunk when coming in contact with blood, with blood being slightly alkaline and milk being slightly acidic.
The fact that it was spoiled means that you could very well be battling sepsis soon. Sid Vicious shot up with 7 up and vomit, so crazier things have happened.
May I ask why you decided to shoot up with milk? I would honestly use spit before I would use milk.