This is pretty common and can be associated with rosacea (which I have). Yes, after using my warm eye mask, I could express thick matter from those oil glands. I used a couple of cotton swabs soaked in very warm water. Probably not for the faint of heart, but being a nurse, I was comfortable with it. I also was not getting styes, but meiobian cysts that became infected. Never needed injections, but did use antibiotic/steroid drops. Still do when my eyelids are particularly irritated.
I presume you’ve been seeing an ophthamologist, not just an optitian.