There has to be something like that, and probably more, going on if you need 20 pounds in a freshwater pool in a 3 mm shorty and are reasonably athletic in build. I think if we add all the different factors mentioned previously together to come up with the greatest weight need, you should not need 20 pounds. In exactly the same situation you describe, it is unusual for me to put more than 10 pounds on a student. From what you describe for yourself, I would probably have started you with 8 pounds, assuming you would be a bit heavy. The second day of class, after you are feeling more comfortable, I would expect to take some weight off you. I have been fooled before, but never by that much.
I am 6-0, 205. In the pool with a 3 mm shorty, I wear 6 pounds. That is because I want to be overweighted in case I need to deal with a student problem under water. (I may need to control an ascent.) I can actually dive in the pool with a 3mm shorty and an AL 80 with no weights at all.
I would really like to be there with you to troubleshoot the situation.