Will this problem interfere with acceptance into university?

i am currently in grade 11 and i just wrote a final essay for an advanced placement english class. my principal just called me and told me that another student had some exact material in their essay that i had in mine, and this is just 'too suspicious to let go', so i am being accused of plagiarism--falsely accused, might i add. however, they are giving me the chance to rewrite it under supervision. i am prepared to accept the offer to rewrite it and not argue with them, because i'm lucky they're giving me the opportunity to rewrite and not just give me a zero. but i do have one question. i am planning on going to university after grade twelve to join the medical profession (i have very high marks and plan to continue getting good marks) but i've been told that universities can see things like suspensions and what not because its on your record or something? i was wondering if this accusation will go on my 'record', and if so, will this interfere with my acceptance into university? thank you so much for your help :)