Yes, I would be very careful about handling her, or letting her too near Oliver until she's been checked by a vet or a clinic - fleas in HIS fur would be a disaster - so hard to find! So good for her that you found her, plenty of liquids are important, as someone mentioned dehydration ... I'd return the shampoo, get the spray, but the green goo sounds like infection in her eyes (don't want Ollie-boy getting that either - so she should see a vet soon. (Wash your hands after playing with her before touching Oliver).

Perhaps you can tell your parents that it's temporary, and if she gets healthy you'll find her a new home. Then, if they fall in love with her while you are getting her healthy, she might get to stay anyway!

Good luck and keep us posted!