Painless tiny lump on eyelid rim for 2 weeks (about 2 mm), also no swelling but daily eye-headache. the part inside eyelid is whitish, outside it has eyelid colour with a bit of red around the little lump. warm compress didnt help. what could it be?

Sounds like a sty but there are several other possibilities. You need to have a doctor look at it (virtual or in person) before making a “real” diagnosis and suggesting treatment

What you describe is consistent with a stye. Because the lesion has not improved with warm compress and persisted for 2 weeks, it needs to be incised and drained (I&D) by eye doctor.

Also your ophthalmologist can inject the chalazion with a small dose of kenalog which will solve the problem,