With my dog behaviourist hat on...
Flooding, ie, dropping the subject in at the deep end and exposing them to the thing they're scared of with no escape... is a REALLY bad method of fixing phobias/anxieties.
I would not do it to a dog, it is not hugely useful in people and thats before you come to the issues that can arise when a human misunderstands a dogs behaviour and body language.
Next - puppies are HORRIBLE bitey squitty pissing machines that NEED you and your comfort and your attention an enormous amoun in the first few months - they are a lot like newborn babies except 1/ they bite and 2/ you won't be tolerated in not doing stuff because of the puppy/bringing the puppy everywhere with you, as you would with a baby.
Most people who get a puppy get whats called 'puppy blues', it is a similar thing to PND.. hormones rage (puppies often trigger the production of oxytocin in humans... some people react badly to that) some folk can feel absolutely AWFUL... and then the puppy trundles around the house crying for them, weeing everywhere, chewing stuff up and biting them.
In your shoes..
Find a local dog trainer, look up Puppy School, puppy school trainers are typically kind and force free - explain that you'd like to sit in on a few classes to help with a phobia, if they've room for an adult in a corner, most will happily oblige.
If you ask for it, you can sit in a corner near a door, with some tables on their sides so you're in your own little space and no dog can come up to you (they'll be on leads anyway!) and get used to seeing dogs and listen, learn a bit about dogs too.
Take it from there...
But please, do not go and get a puppy to fix your phobia (and definitely do not go and get an adult dog!) - the ways in which this can go horribly wrong are myriad, and it will be the dog who suffers in the long run.