You can't achieve the sexual satisaction you would like because your lack of a partner, masturbation can relieve some of the stress but it's not the full potential your sexual happiness can reach.

There's nothing wrong with masturbating, and there's nothing wrong with touching yourself and having fantasies in public. It is likely a strong indicator that you are bored with your nonexistant sex life.

I'm 19 and in the same boat as you are, but I am opening up to trying new things even without a partner: porn, toys, lingerie, and fetishes. It gets the job done, but I'm not nearly as satisfied without a partner, as I am also a virgin.