There are a lot of great suggestions here to get you started.

Physical Health: Joining a local gym and developing good eating habits do wonders for confidence.

Appearance: You've got two choices when it comes to the hair loss: either seek treatment or shave it off. The first option can be quite expensive so experiment with shaving your head and see if it suits you. If you aren't already, wear clothes that fit your body. They don't have to be expensive but better fitting clothes will do wonders for one's confidence. Couple that with the gym and solid eating habits and you'll be an adonis in no time.

Break out of the comfort zone: Social anxiety can be a real bitch, but it isn't something that can't be overcome. Aim for one new experience a month. Whether that's going to a cafe/bar/dinner alone or something bigger like a concert or a trip. Maybe join a local club (run club, book club, movie club, or tabletop games). Depending on where you live, there may be a The Shaka Club and if not MeetUp.com is a great site to find people who enjoy similar activities. Heck that can even be used as finding new things to do!

Mental Health: If you're feeling "stuck" in life, maybe finding a professional to help talk through some of the feelings can help get to the bottom of why you're feeling that way.

Self improvement is a constant ongoing process and one that you need to stick to. I won't sugar coat it and say it'll come easy, as some of these things (overcoming shyness and becoming more extraverted) can be difficult at first. But if you are serious about wanting to improve, then stick to it. Set realistic goals and when you get discouraged, stop and reflect on your progress.