Dear Betty,
There was no 36th Texas Infantry Regiment; however, there was a 36th Texas Cavalry (sometimes called the "32nd Texas Cavalry") but they did not fight East of the Mississippi. The location at Vicksburg you recall is named the "2nd Texas Lunette" and was held by the 2nd Texas Infantry during the siege. (Here is a link to the Vicksburg Nat'l Military Park and this Tour Stop; http://www.nps.gov/vick/ts_12/ts_12.htm )
If you'd like to read more about the 2nd Texas Infantry, here are some links.
http://www.2ndtexasinfantry.com/
http://www.cba.uh.edu/~parks/tex/irg0020.html
http://www.tsha.utexas.edu/handbook/online/articles/view/SS/qks4.html
Jim Martin