I went to a job interview specifically telling them that overtime is a dealbreaker for me. They assured me that they don't make people do overtime, but so far I do almost every day. What should I do?

Set your boundaries and communicated about it. if there is no way for a compromise, then leave

My immediate reaction to your post is; “Come on who are you kidding! A design job without OT? That’s like KFC without chicken!”

Onward to solving your problem; I suggest that you flag it up to your boss to ask for more design related jobs. Behind their back you look for another job with preferably a better salary.

Alternatively if there is a new project you could volunteer yourself to take the designing for the new job. Sometime you’ve got to ask for something to get it.

Noticed this was posted late last year. Hopefully your situation has improved, otherwise it’s time to make a move. (But remember to quietly get the new job first before resigning)

Definitely speak to your bosss about it.
Long story short: If they love your work, then they should be more respectful to their employees in terms of time and effort.
Are there other alternatives outside the firm that you can consider? If your skills are also recognized in other firms, and they have bosses with more integrity, than it might be an option to move!

Work over time on what u don't like to do? The option is obvious.