From what you have said you clearly don't want to just throw this away and would like to try and advance things so why don't you just discuss it with her and let her know what your expectations in a relationship or wife are.
At the 3 month mark emotions should be fairly high so i find it odd she doesn't want to hold your hand or hug in public and fuck like crazy out of public. I get it some girls may not put out but personally I've never come across a girl who doesn't after 3 months of dating* and unless there was a clear reason they weren't I wouldn't be keen on continuing.
But i don't thhink you should just throw it away and would be a dick move to do it on valentines day(unless I misread and valentines day has you thinking about things to do later).
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