There's nothing wrong with giving an injection yourself, IF YOU KNOW HOW. OP has clearly had it explained correctly, so it's not an issue in this case. If you don't know what you're doing, properly, with injecting horses, then yes, you CAN kill the very animal you're trying to help - depending on the medication you're administering. You need to be VERY careful with penicillin, as mentioned, and a lot of other things as well.
If you're ever not sure, ask your vet. They will know. It's what they're trained for after all!
A CLEAN SLATE FOR THE FUTURE