Cuddling before bed


So when I started dating my boyfriend he expressed to me how he wasn’t too fond of cuddling right before bed because he can’t fall asleep. While I am completely okay with that, I do not feel the same and I don’t know how not to feel like I’m getting the cold shoulder when he turns away from me in bed. Realistically I understand his reasoning but emotionally it’s causing a little bit of inner turmoil. We got into a little bit of a fight last night and I brought it up, so later when we were falling asleep he tried to cuddle me, but it felt like he was only doing it so I wouldn’t get mad. Am I just overreacting? Or is there a way to make us both happy while falling asleep?

Edit: last night was the first night we’ve slept in the same bed since my confession (we don’t live together) and he made sure to be touching me all night, cuddling me for the majority of the night. I don’t know why I didn’t say something as soon as it bothered me because he’s the most understanding boyfriend I could ask for. Even if some nights he’s not as affectionate as that, it feels amazing to know that he does truly care. Thank you all for the help!