Swarms can happen earlier and later (and do) than the dates I'll mention but for north Texas (DFW region), my experience has taught me the peak swarming season is about a six week period from around the first of April to about the middle of May.

Last year, my biggest swarm week was March 1st! I was stunned, caught me off gard. In checking my hives this past week, they are not anywhere near like last year, barely any brood ect.
I am watching close this year, just in case...
I am on I-20, 100 miles East of Tyler.