I see students go through what what you describe all the time. I don't think it is unusual regardless of how you perceive your maturity level.

I think true maturity is learning to embrace that stuff without letting it worry you that you should be too old for it. Like you, I was always considered old for my years, and this came from the fact I was never allowed to be a child. But, I never felt I was allowed to be an adult either when I was younger and as a result I was filled with adult ideas but not listened to.
Then as I got older I hated being thought of as childlike. I'm just starting to realise it is ok to care about makeup and things. Never too old!
The mood swings and anger might just relate to becoming more aware of your emotions - not necessarily being teenager-like but exposing feelings that were always there and making them closer to the surface. Therapy certainly has done that for me, and sometimes I surprise myself with how much emotion I can actually express in situations where previously I would have felt nothing.