Ready meals, I had one of those little white lumps on my lower eyelid and like you, picked at it until it came out. A tiny pin prick of hard white stuff. It left a tiny crater that never closed up.
When I next went for an eye test was told to see my GP about it.
GP referred me to an opthalmic surgeon who told me it was a basal cell carcinoma and would have to be removed.
They are not the kind that spreads but can go deeper so need to be taken out.
I ended up having two ops as the biopsy revealed it was bigger than initially thought. I had to have a skin graft and my eyelid sewn shut for six weeks. I'm due for my five year check next March when I hope to be signed off.
So, please don't assume these little spots, swellings etc can just be ignored. Get them checked out.
I also had monthly injections in the other eye for macular degeneration, now stable and it's really no big deal, so don't be put off by the needle thing. Your eyes are precious.