Getting into biomedical engineering at Texas A&M probably requires hitting the automatic admission college GPA of 3.75, since hardly any are admitted without automatic admission. See TAMU ETAM statistics - #172 by pbleigh and following posts.
So unless he is willing to take a less competitive engineering major at Texas A&M, it may not be a good idea to choose Texas A&M if there are other choices.
Purdue has a similar system, but the automatic admission to major college GPA is 3.2: Enrollment Management Policy for FYE Students - College of Engineering - Purdue University
Remember that earning a 3.2 or 3.75 college GPA is typically harder than earning those GPAs in high school.
But why not take IIT full ride or UT Dallas in-state cost with direct admission to the major? It looks like you are concerned about costs at Purdue, so if it is too expensive, then he still has some choices that cost less and do not have the likelihood of not being able to get into the major.