Did you mess up by taking her hand and holding it......twice in one night? I would say you didn't mess up her, but you sure messed up yourself. How? Your mind has given way too much time rehashing it, and your thought have gone from holding handing to thinking about initiating sex.
James, the thing for you to do is act as if nothing eventful ever took place. She should be the one getting her hopes up that it signified something more may be on the horizon. However, that is not the case. You are the one who continues dwelling on those thoughts, and it is a waste of energy.
Initiating handholding is pursuit. You need to stop pursuing her.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!