Cleansing oil and balm makes me breakout

It happens. Some skin clogs from oil or balm cleanser no matter how much they rinse it properly. It's a trial and error. You should try if micellar works for you better or double cleansing with your facial wash. Is your sunscreen waterproof? Do you wear makeup? If both are no, then just using one facial wash is fine.

what oil did you use? and how did you use it?

Maybe your skin just didn't like that particular oil cleanser. The same thing happened to my friend. She switch to a different brand and has had good experiences with the double cleansing.

Actually, it kinda does, but I use the trick of not letting it stay above 20 seconds before washing it off

Try using a Micellar water to compare. Also, do you wash off with a cleanser afterwards.