First I would re word mental illness and say a mental health condition or concern. It's true you can be classed as Ill when in the throes of mental symptoms but if it's something long term it is a controllable condition.
You might just be that type of person who needs their "me" time. Or you may in fact be depressed. When I was clinically depressed I wanted to be sociable but just couldn't be. My teenage self is a bit like what you are describing. I would get in touch with doctor, to be on safe side. Best of luck. People invite you out so obviously enjoy your company on the plus side!