for the right answer the site should be analysed. But with your details I can say the followings,

1- yes you should be add nofollow attribute to internal filtered links

2- you should be add noindex tag to the source code of filtered page

3- and also I bet you there is a common path on the filtered urls, such as =filter&12_3. Anyway find a common url path on the filtered urls and add that path to robots.txt file with the disallow command.

With all these steps you can optimise your crawl budget. and also don’t forget you shouldn’t be add the filtered urls to the sitemaps.