Hi is it better to brush teeth today on a fast day,or wait until on Shabbat? Since by then it will be really difficult to just use mouthwash.

ב"ה Shalom Although, I assume your question was asked before the 10th of Tevet, it only reached my desk today. The Mishna Brura ( 567:11) writes that in a case of discomfort, one may rinse his mouth on a fast day, and one may do so even on Tishah B'av in case of great discomfort. This is correct as long as he makes sure not to swallow from what’s in his mouth. However, one should be more stringent and not do so. It would have been better then to brush your teeth on Friday the fast day, rather than brush your teeth on Shabbat, which is something many refrain from even without toothpaste. (See Shemirat Shabbat Ke'hilchata Vol. 1. Chapt 14, 39. ) However, If you follow the Sephardi custom, according to Rav Ovadya Yosef zt"l (Yabia Omer Orach Chim Vol.4: 27) in case of discomfort one may brush their teeth on Shabbat even with toothpaste. All the best