The link below finds a list of the sessions and dates of the first through the current Congress, 1789- present. The list is at the website of the U.S. Senate.
Since 1934, the first session of a Congress convenes on January 3rd of odd-numbered years and adjourns on January 3 the following odd-numbered year. (For example, the 116th Congress began January 3, 2019 and will adjourn January 3, 2021.)
The Congressional Record holding at Adams Library and on the Web.
The Congressional Record is the official record of the proceedings and debates of the United States Congress. It is published daily when Congress is in session. The Congressional Record began publication in 1873 and is still published today.
At the end of each session of Congress, all of the daily editions are collected, re-paginated, and re-indexed into a permanent, bound edition. This permanent edition, referred to as the Congressional Record (Bound Edition), is made up of one volume per session of Congress, with each volume published in multiple parts, each part containing approximately 10 to 20 days of Congressional proceedings. The primary ways in which the bound edition differs from the daily edition are continuous pagination; somewhat edited, revised, and rearranged text; and the dropping of the prefixes H, S, and E before page numbers.
HathiTrust is a partnership of academic & research institutions, offering a collection of millions of titles digitized from libraries around the world. This link is to a catalog record in Hathi which provides links to CR vols from 1873 - 1993. See, specifically, the holdings from the University of California which provides the vol and part numbers and has the most complete collection available. The CR Index volumes in most cases should be included here. Sometimes "Index" is stated