You
can be happy, but you're not going to be if life feels like an unbearable burden. It doesn't have to though. Can you seek out professional help? I think you should do so as soon as possible, especially if you're having suicidal thoughts.
Bucking the social pressure regarding the stigma of being short isn't an easy thing to do when you're down but people who judge you for it are probably not worth knowing. Don't beat yourself up over it, being short isn't a crime. As for your personality, those all sound like endearing qualities to me.
At any rate, being picked on is not your fault; no one should do that regardless of what someone's personality is like. And whatever it is, I'll bet that you're a better, nicer, and more charming person than your depression allows you to give yourself credit for.
I've been in your shoes several times. For all those times except my most recent spell, I decided to ride out the misery alone. It sucked. So when it came back this time, I decided that I didn't want to struggle through it alone, especially when I had ready help at hand if only I bothered to seek it out.
It can get better, but you need to muster up enough appreciation for yourself to seek out opportunities to make it better. Good dietary habits, regular sleeping patterns, exercise, venturing out into the sunlight, and being social all help a lot. Doing them on a sustained basis does require a certain amount of willpower, which can be difficult to muster but isn't impossible. I didn't think I could, so given all that, going to see a counselor was actually comparatively easy.
Oh, also, don't tell yourself nothing will work from the get go even if it feels like that. All these things can and do help most people tremendously. And even if you feel alone in this, you're not.