じゅうじゅつ is different from じゅうどう. They are usually written in kanji. 柔道 is made from 柔術 by Kano Jigoro at about 135 years ago. 柔術 is a martial art from the old days and Brazilian jiu-jitus is known in Japan.

わかりました ありがとうございます! Is it perhaps more normal to use kanji for "jujutsu" and "judo" in Japan?

I know it's said じゅうじゅつ in other countries, however, we generally say じゅうどう. I think in writing, きょう、じゅうじゅつのれんしゅうにいきます would be better. (Today, I'll go to practice/train Jiujitsu.) *れんしゅう(noun) = practice/exercise/training/etc depending on the situation.