Ramadan - Sawm or Salah?

Last night I made niyyah to fast today ('Ashura), thus making it an oath to keep this fast. Since I don't have my alarm clock, I made du'ah that Allah (swt) would wake me for suhoor. I woke up about two minutes before adhan-al-Fajr, so i wasn't able to eat. I went back to sleep afterward, waking up at sunrise to notice I had a nocturnal ejaculation (wet dream). I'm pretty sure this doesn't make the fast batil. So I continued fasting. Upon coming home from school I would have made wudu and performed salat-al-'Asr, when I realized I needed to make Ghusl to pray (which would break the fast.) Since I'm not ill or travelling, Salah is fardh. Am I to break the fast (and oath) to pray 'Asr, or am I allowed to make qa'ada afterward to keep my oath (and fast)?