A Lucky Draw

Tonight's club game was a real stinker, and I really hesitate to post it - I was (much) worse for most of the game, then managed to escape with a draw, but not before missing a few chances along the way, and a little kerfuffle about the drawing rules. 

Anyway, I suspect this isn't the first game on the bottom board of a chess club to produce some confusion around the drawing rules. It was only after 28.e4 that I began to recognize some chances to save the half point, and after blundering away a couple of chances to get it, I finally caught on. Once it looked like I had the king cornered, I thought I had nothing to lose by holding out for another mistake and played a few of the checks! Not sure about the etiquette of that, but I got the feeling White didn't like it. We agreed to draw at the end, and I felt lucky to have survived 13...Ne4??