As everyone has said, saying an Act of Contrition directly to our Lord is a great start.
I can say from experience that our parish priests are awesome when it comes to hearing confessions outside of the normally scheduled times. I bet most priests are pretty good about this too.
I have done this on three occasions. Once, about 15
mins prior to mass, I walked up and asked, “Father, can I please trouble you for a two minute confession?” Done. The second time, I called the parish office, identified myself, (ooops) and asked if any priests were available for a quick confession. They said they would check. I thought, “Oh great! They’ll tell the priests who it is and they all run out of the office!” Well, the same priest that I confessed to the night before (yes, less than 24 hours earlier and face to face) answered the phone, identified himself, and asked “Can I help you?” I almost started crying. I said ,“I messed up” and asked if I could make a quick confession. He asked me when I wanted to come in and said he could do 7pm, now or whenever I wanted. I told him I was 5 mins away. He said, " Come on over." He had a box of Kleenex waiting for me and asked, “Do you need these?” Done. Today, I went to another parish that has 6:30am daily mass and Mon thru Fri 7am Reconciliation . Done.
The truth is, I have needed to go since Sun night. I wimped out a couple of times at my own parish. I didn’t want to wait until Tues next week.
The moral of the story is if a priest at your home parish can’t, another parish may have a more diverse schedule or like some else said, grab a priest before or after daily mass or call the parish office. There is almost always a way. I consider mortal sin to be a 911 of the soul and I don’t believe such things should wait.