Yes, yes, yes!
I'm the shy girl who was always afraid of going out alone. And because I had only a few friends (or none, at some points), I stayed at home a lot! Then I said **** it and just went alone! I go to eat alone, I go to the cinema alone (why do you need someone to go to the cinema with, anyway? you're just gonna be there, in silence, in the dark, for like 2hours), I travel alone. And you know what? I love it! I love doing whatever I want to do, pick the places I want to go to at the times I want to go, eat what I want, watch whatever movie I want (usually chick flicks, of course ;) ).
Life is too short to wait for others! So go out and live! If you have friends and want to go with them, great! If you want to go alone, also great! Do whatever makes you happy!