Born in Saratoga, Texas, Sheehy received a Bachelor of Laws from Baylor University School of Law in 1934.
He was an assistant attorney general of the State of Texas from 1934 to 1935.
He was in private practice in Tyler, Texas from 1935 to 1951, interrupted by his service in the United States Army Air Forces during World War II from 1942 to 1945, where he achieved the rank of Major.
[1] On May 16, 1951, Sheehy was nominated by President Harry S. Truman to a seat on the United States District Court for the Eastern District of Texas vacated by Judge Randolph Bryant.
He served as Chief Judge from 1954 until his death on February 23, 1967.