Hi and welcome to the forum! I am glad that I can help you.
You would like to know whether the spongy round thing that you feel when you touch your armpit is infection of the sweat glands.
Sweat glands infections are common and appear if the level of hygiene is low. It may also appear after cuts during shaving the armpit which is common in women. It can be presented as a small pea-sized thing or as big as a chestnut filling the entire armpit area. It may be colorless or accompanied with swelling and redness if it has grown bigger. Due to the infection, pain in the armpit area appears and may sometimes be the reason why people save that arm and shoulder from any movement. It is treated with antibiotics with a wide range. If the infected sweat gland gets to be the size of a chestnut, or even bigger, a surgical procedure is recommended then to drain the pus.
Given the symptoms that you describe, a small spongy rounded change in your armpit area that reduces in size after administration of antibiotics, it is likely that you experienced a sweat gland infection. You may consider consulting your doctor for further information about treatment options.
Please keep in mind that I provide medical information only. I am not able to diagnose medical conditions online. Please contact your doctor for further advice or information about treatment options.