Simply put - you should go at the next available opportunity. Sometimes I do intercept a priest either before / after daily mass and ask, and they’re always very happy to do so, but I also understand that it means revealing my identity and it can be a minor inconvenience for them. If you choose to do this, just remember to keep it very brief (no more than 30 seconds to rattle off your sins).
However - I do think it’s reasonable to wait until an appointed time where you can ensure anonymity. I wouldn’t say you are obligated to go before a scheduled confession time that you can reasonably make. Scheduling also comes into play - I don’t think it’s necessary to cancel an event or other obligation to make confession.
Notice - a lot of these are “I think” or “you should”, there is no specific criteria or guidelines laid out by the church on this subject. These are just good rules of thumb that I’ve come up with that seem reasonable.
One other thing I do, that you might find helpful - Whenever I find myself in a situation where I feel I need to go to confession, I pray three Hail Marys and ask the Blessed Mother to help me get to confession. I promise her a rosary dedicated solely to thanksgiving for her intercession afterwards. That’s always helped me get to Confession quickly, even if it seemed like it would be impossible.
I hope that helps! Never despair and trust in God’s wondrous mercy!