I am sorry you are having difficulties. Being a teenager is hard, as is being a teenager in high school. You are taking care of yourself by exercising and eating a a healthy diet. Good for you! It does help to talk to people. Are you able to communicate your feelings to your parents, other family members, or friends? Having one other person to confide in can make a huge difference.
I understand how your situation would be troubling to you. Looking people in the eye is uncomfortable to a lot of us. I make a point of doing it when I talk, but many people don't and are visibly uncomfortable. Two of my son's teenage friends avoid conversation and seem to feel very awkward when asked questions. They do not make eye contact. So, if you feel uncomfortable, then have physical manifestations of that-blushing, watering eyes, it sets up a cycle. You are now hypersensitive to any situation that may bring these symptoms to the surface. I think the same for the tongue issue, and the yawning and twitching.
I definitely do not think you are going insane. I think a lot of people have varying degrees of issues like this. I suffer from general and social anxiety. I also have hyperhydrosis (sweaty hands). My hands can be completely dry, and if I think of something remotely uncomfortable, they sweat in a matter of seconds. If I am nervous, the sweat can run down my arms. At least no one can see that, but it's mighty embarassing to shake or hold hands.
You are reaching out here, so you are obviously at a point of wanting to do something to to make your situation better. In my experience, doing nothing only makes matters worse. My advice would be to talk to someone about how you are feeling. Maybe you could ask your parents to set up a doctor's appointment just to make sure you have no health issues. You could always bring up your concerns there.