This is a picture of it
Yes- it looks like an acne nodule. Is it extemely painful to the touch? You might take a break from the acid peel (this can really aggravate nodular - cystic acne) and see if the inflammation reduces a bit. You can also go to a derm and get a cortisone injection to reduce swelling. Intermittent heat helps bring the infection to the surface to drain. You can try applying heat for about 5-10 minutes as many times as possible throughout the day, it can also help with the pain.
Its a cyst. Inflamed as well. Do not try to lance or poke it that will make it worse. Dermal cysts like these will scar easily if you do to much to them. Ice and anti inflammatories can help. This being ibuprofen and histamine blockers like benadryl can help and provide some relief. Apply an acid most like will not help. The cyst needs to come to a head and drain. Applying moist, warm compresses can hasten this process. But i have found this to be slow. For me BP and differen cream helped speed up the process to which these things go away. Sometimes if i can feel that they have a lot of pressure i will take a klenex and gently apply pressure. Sometimes they rupture and drain, becoming smaller. Other times this does not work. I do not force. I just let it pass.