I would use the latter choice. The reason is, if you say "I will", that assumes you will definitely be a doctor or will be accepted. It may sound a bit arrogant. If you say "I would", that means if you were given the chance to be a doctor, then you would do the following.
I think the correct word is "would" simply because you haven't been accepted yet. If you were accepted, you would use the word "will".