I have been caught out, and a number of my friends also, when trying to give another character morphine and ended up giving it to myself.
The two (Apply and Inject) options in the context menu do not give you any clue as to who will receive the morphine, If it is the first time you have tried to do this then all you can do is guess which one gives it to you or to your friend. Its a 50/50 chance as either could apply.

I would suggest something like the following:
Apply Morphine to <Name of person interacting with>
Inject Myself

I am guessing that the same issue may be encounter when giving Epinephrine?