'Catched' is often mistaken as the past tense of 'catch'. This is a mistake! The past tense form of 'catch' is 'caught', as in “I caught the ball”.

Can you use catched?

Catched is perfectly fine to use and has been in the english language for a very very long time, so long in fact that we actually rarely use that past tense and now prefer to use Caught. However, using Catched is perfectly fine and so is the abbreviation catch'd.

Is catched up correct?

"Caught up" is correct. I'm not sure "catched" is ever correct. Merriam-Webster lists it as "chiefly dialectal". Caught is the 'standard' past and past participle of catch now, but it wasn't always the case.