How to deal with strong physical attraction and my bodies reaction

For context I'm a man. I'm getting into a relationship that is headed towards serious territory. We are getting emotionally close, and that is new to me. When we have close physical contact such as cuddling I become fully hard for the entire time. This is embarrasing because it feels like an inbolded message that I am horny, and this intimate moment means nothing to me. Sometimes even a touch will affect me. I had an average sex drive before her, but now it feels like it was dialed to 100. Do I just let it bulge everytime, bring it up casually, or try to hiding it the best I can? I really like her and don't want to mess this up.