It is possible to correct a clipped coat but it can take up to a year of patient handstripping whatever coat will come out every 8 weeks. It doesn't all loosen together and stripping is about pulling out only the dead coat - which is why it doesn't hurt! :rolleyes: The idea behind stripping isn't just for the look of the dog, it's for practical purposes, leaving the dog with its weatherproof coat that it was born with.
If a Westie is bred with an incorrect coat, ie, soft, thin, no undercoat etc, then it's still possible to make it look better than whacking clippers on it, but it's a skill that doesn't appear to be taught these days! :D I hope that you can find someone with the experience to help you and your dog.