I'm new to shorthanded also and the first time I read this without reading everyone else's responses I saw a screaming bet on the turn. I think you are right when you say that checking the turn tells everyone that the Ace scared you and you want to see what everyone else is going to do. I would bet this and fold to a raise. That is probably why the SB led the bet on the river because he knew you didn't have the Ace, which then he knew that his paired Jack at least stood a chance to the showdown.