Welcome to JustAnswer, and thank you for your question.
Unfortunately as we age, our skin becomes very fragile due to losing the fat layer underneath the skin and some of the connective tissues. There isn't much you can do to improve that, except to make sure to keep your skin well moisturized. This will help a little to keep it from tearing.
Use a moisturizing body bath lotion rather than soap (Dove is a good one, but there are others), and a good moisturizing lotion right after bathing and once or twice a day. Pay special attention to the areas that are exposed the most.
Wearing garments that cover your arms helps, but may not be practical in the summer.
When you do injure yourself, you need to be very careful with the cleaning and treatment of the wound to speed healing and prevent infection. It's not good to leave these type of wounds open as they can become infected very easily. You will need to get some supplies to keep on hand. Ask the pharmacist at your local pharmacy to help you locate these items:
When you tear the skin:
Repeat this only once per day until it is healed enough to leave the dressing off. If the dressing sticks a bit, use the peroxide/water mixture to wet it to loosen before trying to remove it. When the wound is either completely closed or solidly scabbed, you can leave the dressing off. Then just keep it clean and dry.
I need to add some other things:
Make sure to pay attention to your diet. Plenty of protein and fluids will help. A daily vitamin supplement also.
And very important, if you every notice one of your wounds become reddened around it, swollen, hot, having discharge or becoming more painful, see your doctor right away as you may develop cellulitis ---a very dangerous infection.