Here's the deal. You have to accept yourself, your body and where you are. When you treat yourself gently and with love, you will enjoy exercise more and get to your goals faster and with less anger.
1) Other people aren't looking at you. They don't care. They are thinking about their day or their relationship or their workout or their own selves. People think about themselves WAY more than they think about you. You have to let go of the idea that they are looking at the fat person. They aren't.
2) You have to get over the idea that size 16 is that big. You are not as big as it gets. Not by a long shot. This girl is a lot fatter than a 16 and she's working it:
http://www.youtube.com/watch?v=Tbcoh5hre74
3) You have to slow down and back off. Developing fitness comes slowly.
You say you are very "out of shape." If that is true, then you need to back way off and take it slower than slow. When I started running (at a pretty fit age 25), it hurt. I cried almost every day. My goal was just to go a little further every day. I eventually ran a half marathon. I was a high school swimmer. When my husband started swimming laps with me, I thought he was going to barf up a lung. He didn't cry, but I think he wanted to cry. He had to develop that fitness slowly.
You have to start slow. Are you doing a couch to 5k program? If you are, it's okay to slow the program down by repeating a week or adding a rest week or a rest day. The important thing is that you keep doing it. If you suit up and show up and do it consistently, it will get better.
4) This shit hurts everybody. It's just a fact. If you challenge yourself and try to push your fitness goals, it's going to hurt sometimes. After I was 42 or so, it hurt even when I wasn't pushing my fitness goals. Take some naproxen and get on with it. It's worth it.
5) Find a sport that you love. Doing something cool will make the rest of it more tolerable.