That doesn’t seem right. They should have nominated you, and told you to get some more service and leadership activities. Just my opinion, but you don’t bump a 3.9 off NHS unless they clearly continue to violate the terms of the society or something. Hopefully you can be re-nominated as a senior.
You should take dual enrollment because colleges like seeing students who challenge themselves. However, it’s better to avoid classes in your major (unless pre-req) simply because those courses are probably going to be better at the U (which has an excellent psychology dept, by the way). Especially if taken at a cc or a non-flagship school, they might not be as rigorous or well-taught. You do want to be well prepared for upper-division. Finally, you want to make sure you are fulfilling the college prep. requirements that the U and other schools specify (4 years of English, 4 years of math, preferably calculus - though one of my kids did AP stats and got into CLA last year - three years of lab science, foreign language, fine arts, history and social studies, etc). Hence the advice to avoid getting too much into your chosen major while still in high school.
Cultural anthropology, stats, World Geo. are all good ideas for satisfying the Liberal Ed. requirements. Intro to Psych. is fine if it waives your basic requirements for the major. Abnormal psych you might want to take at the U.
Do you have any hooks - URM, first generation student, etc.? Also, are you in-state or OOS?