I agree that you should not try to”prove” that you are straight. On the other hand, though, isn’t it useful for people to be properly informed? Clearly, if she thinks you are gay, she isn’t going to give you anything you can run with. So it would be important that she is clear on that.

Your buddies say she is into you. Her standoffishness doesn’t necessarily contradict that. She might figure that she has already given you signals, such as the laughing. What signals have you given her? Could it be that she is standoffish because she is waiting for some reciprocity? And the weird tension: Same thing. Could it be that there is tension because what “should” be said on your part isn’t being said?