Most people have stretch marks, so don't let those embarrass you.
As for exercising, you do not need to have equipment to get a good workout. First, I would recommend reviewing the Teen's Guide to Fitness & Exercise to get a better understanding of how long and how often you should do both cardio and strength training: teens.sparkpeople.com/resource/fitness_art
In regards to exercising outside, don't let your embarrassment keep you from that either. The thing is, you are deciding to change your habits and become healthy - so there shouldn't be any embarrassment there. Walking is a great form of exercise if you are willing to go outside and give that a try (make sure you get and keep your heart rate up). For inside workouts, you might want to try some of the suggestions from this article: teens.sparkpeople.com/resource/fitness_art
. Also, the workout generator is a fun thing to use (select the no equipment option): teens.sparkpeople.com/resource/fitness_pla
. You can also do some of the workout videos that we have listed in the Fitness section of the Healthy Lifestyle tab at the top of the page.