Dear William -- thank you for posting to History Hub!
NARA Record Group 233 are records of the U.S. House of Representatives, held by the Center for Legislative Archives -- a unit within the National Archives.
Indexes to private claims submitted to U.S. Congress have been published as a part of the U.S. Serial Set. The indexes generally provide the name of the claimant, the nature of the claim, committee of referral, Congress and session, number and nature of report, number of bill, disposition in the other House, and date of the act or other remarks.
The private claims indexes can be found online through Hathi Trust (and other sources, for example I believe they're also available through Ancestry). For House records in the time period you're interested in, see the Alphabetical List of Private Claims presented to the House of Representatives from the 1st to the 31st Congress.
Another resource is A Century of Lawmaking, a website of the Library of Congress which brings together online legislative records from the Continental Congress through the 43rd Congress -- including the House and Senate Journals, and the Debates of Congress.
If you're interested in more background on the private claims and private legislation in the records of Congress there is an excellent article in Prologue Magazine on the topic.
To request a specific petition, please email firstname.lastname@example.org.