I have applied to Oxford 3 times (the first two times for Physics and Philosophy, 3rd time for medicine). On each occasion, I was 100% certain the interviewers had no idea I had applied the year before. So if you want to reapply, I don't think you will be discriminated against for being a reapplicant as they probably won't know that you are.
However, I don't mean to put you off, but think very carefully about whether studying at Oxford is actually that important to you i.e. more important than studying medicine anywhere else. If you get an offer elsewhere this year, you will have to forfeit that offer to reapply to Oxford next year. It's possible that you will then be rejected from all universities next year, end up with no offers to study medicine at all and you'll feel pretty gutted. Also, having been to Oxford on three seperate occasions for interviews, I can tell you the novelty of the surroundings, atmosphere, architecture etc. wears off fairly quickly and virtually everyone I know at Oxbridge is having nowhere near a good a time at university than my friends elsewhere.
Finally, as for the BMAT, Oxford use the BMAT score along with your GCSE grades to determine who they invite to interview - after that, everyone is on a level playing field. The way it works is, they first look at your percentage of A* at GCSE, then they use that determine how good your BMAT score needs to be to get an interview. For example, if you have 100% A* at GCSE, your BMAT score needs to be in the top 60% of scores attained by all applicants. If you have no A* at GCSE, your BMAT score needs to be in the top 2%. Check the oxford website for more details.
Hope this helps. Personally, I wouldn't take the risk of reapplying on a course which is as competitive as medicine, but then that's me.