If the skin has actually lifted and peeled I recommend using an over the counter polysporin gel to soothe and heal the skin. I apply oil to the skin (blot if too much) before waxing which normally prevents any peeling from happening. I highly recommend PFB Vanish for ingrowns and bumpy skin.
I have seen this happen only on a few clients. I use a cream wax specifically formulated for brazilians. What type/brand of oil are you referring to ? Does it work with cream waxes?
I've tried different pre-wax oils and have no particular favourites. Sometimes its the scent that makes me like one over another. I don't use cream wax but i see no reason you could not use oil with it. I use the oil with both honey warm wax and hard azulene. Give it a try in the bikini area and see what you think. Make sure you blot the skin first if you think to much oil has been applied.
Typically you want to use the pre and post products from the brand of wax you are using.