Definitely take her to the vet, she probably could do with a check up and she will definitely need a light sedation and be shaved. Baby oil will make a terrible mess and it's not too good to have her licking it, or trying too. She is too shy and scared for a groomer to tackle the job, and if the mats are bad, she could well have some ulceration you can't see. Cats have extraordinarily fine skin, much finer than ours, and it doesn't take much to cause a lesion or tear it.
Don't forget to put her in a suitable container, if you dont have a cat carrier use two laundry baskets tied together...or use a wicker laundry basket with the lid attached, don't forget plenty of paper/old towels in the bottom...sometimes the timid ones get scared and pee.
Good luck with your cat taming/beautification...would love to see pics. Oh, I forgot...while she's being groomed get yourself a good grooming tool, so you can keep on top of it....Furminator is good, but ask your vet to recommend the right one for her type.