No, with one exception.
Though it is perfectly possible to train your own service dog with the help of a trainer, if you are an individual needing the treatment provided by a service dog, it is incredibly challenging to provide the environment, confidence building, structure, and responsibilities that come with service dog training for PTSD. Training a service dog and using a service dog to mitigate a disability are very different from each other and it is ineffective to both use a dog and train a dog simultaneously.
The exception to this is if you already own a highly skilled service dog who will be nearing retirement, your symptoms are currently under control, and you understand that training a puppy to adulthood as a service dog is never a guarantee.