Yes, the IRS and state government, do keep records. If you don't know what estimated payments you've sent in, you might:

1) Be able to get them by checking the IRS transcript.  One of the options let's you see what tax documents were filed, like W-2's, 1099's, including 1040-ES. See How do I get a copy of my tax return or transcript from the IRS?

2) Submit your tax return(s) without your estimated payments. The IRS will send you a letter stating their records indicate a different tax amount was paid. This will reflect your estimated payments.

You may also look at your bank records or credit card statements, to find our estimated payments.