A tiny capillary showed up out of nowhere on my cheek. Since I don’t have the funds for lasers, can glycolic acid help?

No need for fancy lasers and expensive devices. Light electrodessication has been used for decades for isolated capillaries, as well as dense networks of facial telangiectasias and cherry hemangiomas. Especially for a small area, such as this, it takes literally a second (no exaggeration) to treat and very inexpensively. Make sure that you consult with a board certified aesthetic physician and exercise a healthy dose of caution when evaluating claims for this or that supposedly "next big thing," relatively expensive laser or other energy-based devices. Best of luck to you. 

Hello to answer your question yes lasers are the way to go for this.  However if you don't have the funds its understandable.  We carry a treatment cream called Red Vein from DMK Skincare.  This cream acts as a vasodilator to increase blood flow.  It contains inhibitors to reduce vein redness and dark circles. It will strengthen capillary walls and supports the skins barrier function.  This is a great cream to use to help correct them until you can do the laser treatments.  I hope this helps!

Hello and thank you for your question! Unfortunately, a glycolic acid peel, which is in the family of chemical peels, will not have any affect on the tiny capillaries that you speak of. A Laser such as IPL, which is also known as a photo-facial, Will zap those little vessels up in no time and it is actually more affordable in comparison to other laser treatments. I hope you find a resolution quickly!