Vibrating,this woman at the gym just sounds distracted and maybe she is there to exercise only not to find a boyfriend.I think the way you behaved with her was good,and now backing off is a good idea too.With women you can be too attentive and that usually puts them off,playing it a bit hard to get and not so keen works better.You know the saying people don't want what is readily available they want what they can't have.Hold back a bit to make her do the running towards you,so then you can discern if she is into you or not.This is more general advice than specific to the gym woman but equally aplies to her too.I mean you did ok and are doing ok ,don't worry or beat yourself up.With time and practice you will find yourself becoming more confident.Make sure you are addressing those negative feelings about women being cold and selfish too and finding example of women caring and warm to see women aren't all bad and that you don't need to be resentful otherwise those shadow feelings can come out in you when you least want them to or expect and can ruin something for you.But try not to overanalyze situations, you are doing good as far as I can see!