I've been in that situation and was able to get out.
I agree that you need to be sure you pay on time. Those late payments just make everything worse. I'm not sure how your pay dates align with your credit card due dates, but if you can make your payments as soon as your salary is deposited, that would be best. Definitely set yourself reminders as well.
I know it may not always be possible to make more than the minimum payment, but try to do that as often as you can. Minimum payments are designed to keep you in debt. I think you said that you've gotten overtime pay on a few occasions. I'd immediately allocate that extra money to the credit card. If you get more hours than usual a week, try to use the money towards that too.
Good luck. It's hard, but it can be done.