Sounds like what my sister had. Eye doctor put her on several meds. Are you using any antiobiotic eye drops? It did take several weeks for my sisters problem to clear up.
I remember as a kid getting it in 1 eye & then a week later, the
other eye. It's either viral or bacterial. Just like a cold or
flu virus to the eye. If it's bacterial, you usually have an
ear/nose/throat (one of these) w/ it. It's transmitted person to person quickly. Rub your infected eye, shake someones hand,
they rub their eye, they get it. It starts in the inner lining
of eye & can really go after the white of eye. Dr. needs to
determine viral vs bacterial. Everyone frequently washes hands.
Everyone gets color-coded towels from face to bath. No one uses the universal kitchen towel. Even a quick spritz bottle w/
alcohol in it will help germs & air-dry the hands. Kids rub
eyes & then toys or doorknob. I think these bacteria last up to
2 days on surfaces. Hot compresses (fresh one) ea. time will help w/ meds. Get out the Lysol or favorite dysinfectant & wipe
dwn whatever, including the toilet flusher handle. It will keep
going if one person at a time doesn't get treated & avoid eyes
till gone. The specs on cornea are probably irritation & many
times can really hurt. As a kid, school wouldn't let me back
till it was gone. Wash all towels in HOT water w/ alittle bleach
but easiest is color-coding. Same w/ pillow cases. It's a real
pain. Gd-luck. I doubt that it's the result of the house. Some
bring it home from the grocery store cart-bar & then touches
the eye. Wish you luck.