I'm a little perplexed here.
Shii sure is often way too pushy, overbearing, self-centered and insensitive to Tamaki's trauma. At the same time I feel like Tamaki is so torn between his guilt regarding anything sexual and what he would like to feel. He envies Shii's carelessness and would like to get over his repulsion, but it's so hard.
I think that's why he asked to go through with the one year deal. He wants out of his awful situation and maybe sees that Tamaki makes him progress towards that somehow, even just by making him talk and acknowledge his thoughts, feelings and contradictions...
I hope Tamaki manages to be at peace with himself, whether he discovers that he is asexual (I doubt it) or not.
People, the guy saw his first love/best friend dead with his voice calling out his name, plus his brother being hanged before his eyes superimposed with his girlfriend's image, with drugs in his system, on top of all the crap that was his life.... his