What are these boils that my brother has on his eyelids?

Hello doctor,

I am asking this question on behalf of my brother. He is 37 years of age, 5' 7" tall and approximately weighs 70 kg. He is not on any medication. He is a commercial airline pilot by profession and is perfectly fit to fly. He has recently passed his physical fitness exam that is conducted each year. A year back, there was a boil in only one eyelid. But, the bulge was barely noticeable from outside and even from inside the eyelid. Also, there was very slight uneasiness and no irritation or pain a year back. Since there was very minimal discomfort, he did not pursue any treatment. Now, in the past 1.5 months, he has got boils in both the eyes that are noticeably larger and caused him some irritation and pain. His eyesight is better (same as always) and he still able and authorized to fly. Although we hold neutral beliefs in alternative medicine and believe it might be effective in the long-term, we are seeking quick and efficient advice or treatment. Especially considering my brother's profession and his subsequent flight physical exams that he must clear this coming year. However, we prefer to avoid any surgical treatment unless and until absolutely necessary. I have attached a high resolution picture of my brother's eyes. Please give some advice that you can. Let me know if you have any questions and I will be sure to respond at the earliest. I am not sure whether it is a cyst or a stye or a chalazion or something else. Frankly, I have very minimal knowledge of their differences. Yet, I feel and hope it is nothing severe and can be cured with proper medicines and lifestyle habits.

Hi doctor,

Thank you very much for your prompt answer. We were also suggested to take Augmentin 625 mg and Pantop 40. Is it safe to take them along with your treatment? I certainly do not mean to second guess your diagnosis and I am sorry if it sounds so. But, we were also told that it could be a bilateral cyst. Lastly, in either case, from your instinct and experience, this would not be a major cause for concern for us if suggested medications and remedies are followed. Am I right?