Do you think he likes me?

he probably does like you but because you said he was shy he wont admit it because he doesn't feel ready for it. he doesn't want to wreck the amazing friendship you two have and make things awkward, hes more comfortable just being your friend at the moment, give it time and he just might come around. Don't ask him to homecoming you could ask him if he's going to go but not if he wants to go with you if he wants to go with you then he will ask you to go with him or will just ask if your going that's a sign that he's interested and wants to go with you he just doesnt want to ask you to go with him