"I'm so in love that I can't sleep" may be translated as (난) 깊은 연정으로 잠 못 이뤄 / (난) 연정 때문에 잠도 못 자겠어어어, which is like "I can't sleep because of a love [a yearning]. 연정 is a love of the romantic kind, especially in the early developing stage. This phrase is rather literary sounding, because people don't really use 연정 or 사랑 that much in conversations. In daily life, one is more likely to say: - 그 사람 [여자] 생각에 잠도 못 자겠어. The thought of him [her] keeps me awake at night. - 그 사람 [여자] 때문에 잠도 못 자. I can't sleep because of him [her]. Although these lines don't even mention "love", it is usually obvious from the context.

사랑하다 is still ok, but if you want to be really specific, you can use 사랑하고 있다. 너무나 사랑해서 (혹은 사랑하고 있어서), 잠을 잘 수가 없어요.