Congrats on all your new clis
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Dispute the 30 day late if the error was with autopay and check out the rebuild section on hows the best way to combat the 30 day late if it wasnt your fault.
Getting the increases will help your overall utilization which can help your score but definitely bring down those balances and youll see a better jump. The 30 day late will hurt for awhile. Try and get your balances down to zero when possible so you can use your cards like it was a debit, buy what you can payoff at the end of the month. This way you are showing really responsible use of your credit and may even get better limits.
Again congrats best of luck going forward and hope you get get rid of the 30day late