Thanks for your question and photo. Chemical peels are not generally useful for vascular lesions such as broken capillaries or cherry angiomas. They are better treated with vascular laser or IPL if they are very light and small. You might even run the risk of making the problem worse if a chemical peel irritates the skin and causes the vessels to become more noticeable over time. Use a good sunscreen with zinc and/or titanium dioxide in it every day, and ask your aesthetician or laser specialist if they have any other recommendations based on your overall skin type and lifestyle. Best of luck!
Glycolic or any type of peel won't treat a capillary on the face. It would be worth saving up for a laser treatment which would get rid of the capillary in a single treatment with the right technology. Good luck!