One of my clients is an animal eye vet, you can look at some of the more common eye diseases here: http://atlantaveteyeclinic.com/commoneyediseases.htm
The photos are quite graphic. None of them seems to match your sister's kitty's problem though.
Again, no one here can tell you the cost of the visit as vet prices vary from location to location and we don't know what the vet would have you do. It might be something minor like antibiotics or it may be major like removing the eye.
From looking at the size the eye has swollen to and from looking at photos from my vet client, I would say that the cat is in danger of the eyeball erupting and needs to be seen immediately. Perhaps if you ask your sister to imagine if her eye had swolen to two or three times it's normal size, what would she do? You can also mention that this is a problem that will not go away without a vet's treatment, and the longer they put it off, the more it will cost. Guaranteed.
Here's a guide to when your pet should see and opthamologist (also from my client's site)The majority of the cases seen at Atlanta Veterinary Eye Clinic are referred by a general veterinarian. The referral is made when an ophthalmic problem is either visible or suspected. The problem may range from an ocular injury to a loss of vision. Consulting an ophthalmologist allows the pet and owner to receive the benefits from specialized diagnosis and treatment.
Does your pet rub his eyes often?
Do your pet's eyes appear swollen or enlarged?
Do your pet's eyes appear cloudy or is there any redness?
Is there any discharge in the corners of the eyes?
Does your pet appear to tear excessively?
Have you noticed your pet squinting or keeping his eye(s) closed?
Does your pet occasionally bump into things?
If you answered yes to any of these questions, contact your general veterinarian as soon as possible to facilitate a referral.
Here are some common symptoms that we see at AVEC and problems that they could be related to:
Loss of vision: Cataracts, PRA , glaucoma retinal degeneration or retinal detachment