I was painfully shy beginning at the age of 11. My dad was transferred to a new city because of his job, and I had an EXTREMELY difficult time making the adjustment.
Though I still feel lots of anxiety in certain situations . . . like business meetings when everyone goes around the rooom and introduces themselves . . . I often feel like I’m going to PUKE . . . it’s SO MUCH BETTER than it was when I was younger (I’m 55 now).
One thing you can do is go talk to the teacher in your school that teaches public speaking. They should be able to help . . . assuming you’re not into going to some kind of therapist. If there isn’t a teacher at your school who does that, pick a favorite one and talk to him or her. Maybe they had to overcome the same problem in order to be able to stand in front of the class to be able to teach.
It may help if you make a list of small things you can do to help yourself get over this shyness and just gradually work on your list. You’ve already started that by doing some research and deciding it’s a good idea to work on making eye contact.
Maybe you should just work on that eye contact thing for a while . . . maybe a week or two . . . and then maybe try saying a simple “Hi” once in a while. People like being acknowledged . . . we don’t like being invisible to others.

Believe it. You CAN overcome this!!!! You’ll be surprised at what that will do for your life!!!