You are such a sweetheart for taking this kitty in. I can help you hun. The eye drainage may be due to a cold - but even if that's not the case - you may use Terramycin Ointment on the eye(s)...it starts to work immediately and if you don't wanna get it at an expensive vet there are places that sell it like Tractor Supply...(places that sell meds for animals - even horses...they are like farm supply stores but are so great with ALL animals and pets for all needs, incl. medical needs) - Also, the reason lil' kitty vomitted up her food is simply cuz' she/he was so excited to have good food placed in front of it ... it simply ate too fast and therefore threw it up - I have worked at 3 vet clinics...God Love yah hun and God Bless...P.S. If there is no worm (ringworm) or fleas present, you and your lil' child should be just fine...Jodie Erica... Oh, and if there is ringworm or fleas present - those situations can be taken care of without hurting you or your lil' one...Good Luck Hunz ... View related article.