You're not clingy, telling yourself that is self-defeating. At 21, you're not fully formed yet! I can almost guarantee that whatever relationship you're in now will NOT be the relationship you'll be in 5 years from now if that helps you relax a little. You have a whole lifetime ahead of you for seducing and being seduced.
Sound like you might have what they call an "anxious" attachment style. As do I. The way to be less "clingy" is cultivate your own garden: form friendships, have hobbies and interests, have lots going on in your life outside your relationships. Be warned we "anxiously attached" tend to get involved with "love avoidants," who bring out the worst in us.
I'm assuming he's aware you would like something less casual with him, and he's just not on board. If you're not getting what you want from this relationship, you're choices are 1) lower your expectations, and enjoy a casual relationship. Date others. Don't try to fake it, though, if that's not what you want. You don't want to be hurting and pining and hoping for him to come around to love when that might never happen. 2) Walk away, tend to your own well-being, and seek someone who is as into you as you are into them.