Pax, SURE you love me to DEATH LOL :>)
To reduce your risk of vaginal thrush:
wash your vaginal area with water and avoid perfumed soaps, shower gels, vaginal deodorants, or douches
avoid latex condoms, spermicidal creams or lubricants if they irritate your genital area
avoid tight-fitting underwear or tights
wear cotton underwear and loose-fitting trousers and skirts
You all know I love gymdandee to death, but most of the above should be disregarded. Creams causing a yeast infection? Uh, no, unless they're antibiotic creams that somehow got all the way into the intestinal tract. But only the person posting knows how serious this cut is, and none of us here are doctors and none of us has seen the wound. If you think it's serious, see a doctor.
using peroxide on a wound can actually harm the tissue around it and delay the healing process.
Although it should heal, there is always a risk of infection because of all the bacteria that live down there. Be sure to keep it clean and wear cotton panties to let things breathe. Don't use any scented soaps of douche products, as those can actually increase the likelihood of an infection. There's also a chance that it might not heal properly, causing an ulceration or a permanent 'tear' if the two pieces don't heal back together. This is only a major concern is the tear is large, though. If its small, it should be fine.
I wouldn't recommend putting any creams down there unless directed by a doctor, as the vulva and vagina are very sensitive to foreign substances. Many creams, particularly scented ones, can lead to infections (usually yeast), and cause irritation. Aloe would probably be safe to use, but be careful not to get it into your vagina just in case. Aloe is usually safe for most things. You might want to take some ibuprofen to help with any swelling and ease pain. Avoid touching or rubbing the area, lest you make it worse.
If it isn't healing properly or you notice signs of infection (pus, foul smells, a lot of redness, failure to heal, fever, etc.) go see your doctor. It's better to take care of things early on than to have it get worse.