I sent an angry e-mail to my interviewers about a conflict at my home institution. Could this affect my application?
I had some troubles following your question, but if I understood correctly then I would assume that:


The professor interviewing you is highly confused right now. They seem to have literally nothing to do with your university, the program, you (other than having interviewed you recently), and the person that you accused of being unjust - and yet they are drawn into a conflict that they have no stakes in nor responsibility for.
You may indeed have lowered your chances of getting accepted considerably. In the best case your email would be seen as odd. In the worst case it would be seen as grossly unprofessional, painting you as a trouble maker who will randomly lash out whenever something happens that you consider unjust. I have seen students like that, and I know of no professor / admission committee that wants to bother with this kind of drama.



  However, now that I have calmed down I have realized that I should not have let even injustices affect me and it was unnecessary to email my interviewer. 


I think your reflection should go deeper than that. It is true that part of being a professional is also being able to absorb smaller perceived unjustices like that (empathy and an ability to accept that grades aren't everything helps here), but I also can't help but wonder what you were trying to achieve with this email in the first place. To me (and note that I am only going by your short recap) this sounds rather vindictive, serving no other purpose than to get back at the person not recommending you. If that is indeed the case, you should take a good hard look at your actions in this case and learn from that for the future.