I took swimming lessons at the local Y when I was 19. It’s a great place to start late. Just relax and float; that’s essential. Once you learn to float with minimal effort, you’ll feel more confident.
Good luck! 
@Mika
I had my first swim lesson this past Saturday at the YMCA, one of the first things the instructor had us do is face in the water blowing bubbles and also opening our eyes in the water and blinking it out afterwards.
I learned a basic freestyle stroke but find I still get tired in the water after a bit. I learned the basic safety of turning on your back when you are tired.
Lastly, he had us swim to areas of the deeper part of the pool, that was the most nerve wracking but I just turned off my mind and did it. I found out I can tread water for a couple minutes in the deep end as well, and I feel more confident now going into the pool 
I still have lessons on Saturday this month but I’m glad I’m taking the time to learn.
Thank you for the kind words of encouragement by the way
My best tip is to take your time, especially given your past trauma. Start in shallow water and learn the basics of each stroke, paying attention to treading water since it’s essential for staying calm if you get tired. As you grow more confident, gradually move to deeper areas. Consider a facility with both shallow and deep lanes.
Set small goals such as treading water for a few minutes, then move on to stroke techniques. Don’t rush; when you feel prepared, switch to deeper lanes.
@Valor
Thanks for the thoughtful advice! I had my first official swim lesson at the YMCA last Saturday, and I’m now signed up for group lessons each Saturday.
The instructor focused on the basic freestyle stroke, water safety, and treading water skills. I managed to tread for a full 2 minutes, which felt great!
I also went back today to practice, and I’m feeling okay with heading to the deep end and doing the basic backstroke. I still need to build my endurance though.
Choose a pool where you can stand, so you’re always above water if you start to panic. Just stand up if needed.
Find an old Serbian lady to yell at you until you get your form right. That’s how I learned to swim.
I did the same as you. Try to practice as much as you can outside of lessons; those who only swim during class don’t progress as quickly.