AnnieBrooke is right - I do recommend yoga. You can check out YouTube for videos that you can follow along with to learn how to do it.
Here's also a link to an article indicating a variety of exercises you can do, using only your body weight: https://www.mayoclinic.org/healthy-lifestyle/fitness/expert-answers/body-weight-training/faq-20147966
You can also try some light weights. If you don't have any actual weights use a couple of 16 oz cans of vegetables or bottles of water.
As you get stronger, you can do more reps of each exercise and/or add more weight.
How old are you? I might also suggest that you talk to a counselor about your fear of going out alone. Maybe your parents could help you, or a school counselor or other trusted person.
My friend Barb on this site strongly recommends yoga -- look on Google for "the plank," for example. It helps build your core. And, if you live in a house with stairs, try just going up and down the stairs twice every time you go up or down, just turn around and do it once again, but fast. If you do that every day, it will begin to build your strength.