He is not in 6% of his very competitive HS to qualify for auto admission to UT Austin. I’m pretty sure that the rest of Texas public universities will accept him based just on his scores.
Earlham, which was mentioned by a previous poster is in the top 1% in the nation for successful med school placement, and top 2 % in the nation for top law school placement…
If he wants to swim, you might try backing into schools using the swim recruiting sites. You can compare his times to different swim teams and then see if any of those schools are attractive to him.
You said you were looking for D3 with no scholarships, but you might try some D2 schools. In Florida, there is the Sunshine State conference which includes Tampa, Lynn, Barry, Embry-Riddle and Florida Tech.
Florida Tech has a big psychology program, with an emphasis in Autism, and there is a group of forensic psych students too. It is definitely a STEM school, but he could get his premed reqs in too. I know a few swimmers went to the NCAA finals last year. Your son would get a merit scholarship of about $25k, and maybe an athletic scholarship too. I think the aid at Florida Southern and Tampa would be similar, but the COA at those schools is less.
I just saw your comment about Jewish life, so, I am adding on to my previous response:
Earlham also has a Jewish Student Union, the JCC (Jewish Cultural Center) which hosts a weekly Shabbat dinner, and a residential facility (a house) that Jewish students and friends can apply to live in as upperclassmen.
There is also a Jewish Studies academic department.
http://earlham.edu/academics/programs/jewish-studies/
Many premed students end up with a double major, because as an LAC, Earlham makes it possible for students to pursue more than one of their interests and/or passions. So, if your son is interested in that sort of thing, he doesn’t have to give it up for med school/law school, etc…
twoinanddone: thank you! this is very helpful. he said he will be contacting coaches soon. to be honest, we really want him to swim less and concentrate more on school, but he is very resistant to swim less. currently, six days a week morning and evening practices
BB: thank you! Earlham looks interesting, but I doubt he would agree to a small city college idea.
If he’s in the top 10%, he’s an auto-admit to Texas A&M. If he’s in the top 7%, he’s an auto-admit for UT. Liberal arts are default majors, so if that’s what he wants to major in, he’ll be just fine. If he wants to transfer into business later on, that won’t be so easy to do at these schools.
Clark Univ in MA is known for psychology, and I bet they would be generous
@coolguy40 - it changed to top 6% this year 
Some popular liberal arts majors may be at capacity at some schools and therefore must restrict enrollment.
https://liberalarts.utexas.edu/psychology/undergraduate/admission.php indicates that psychology at UT Austin is such a major, since it requires a 3.25 GPA in major and overall to change into. Presumably, if direct frosh admission exists, it will be more difficult to get into that major than just getting into the school overall.