I understand you, I think. I also want to learn new pieces because either they are challenging, my favourites, or both. But in some way like you, I am also overloaded and I have to keep in order my priorities like ending the major, teaching piano to my students, social service, and ending and polishing the piano pieces I have in case I decide to graduate by doing a piano recital.
I agree with your teacher, because the safe bet is improving and polishing the piano pieces you have instead of learning new ones from zero and which the error probability is higher. Those new pieces could be learnt after your recital.
And we are not alone, I bet that there are many students around the world who also want to learn new pieces, including ones which could show off their awesomeness as pianists, but they can't because of timing and overload of work as well.
There is a manga (and has its anime), Nodame Cantabile, and even though there is some fantasy, there are parts where realistic issues appear, like when the titular character decided to enter to a piano competition in short time, with the intention of getting the first prize, she learnt many difficult pieces, but it was a question of time (and with a mix of stress and getting sick) that she failed and got disqualified because her memory failed in the last round with the last pieces.