Just like parrots, every human is an individual. to have a parrot as a service animal you must be able to stay calm and happy around your bird. You must have experience with the bird you want(and not just a little) if you are going to happy and calm around your bird, then I see no problem. But if you won't be able to fight off your anxiety then I would not recommend getting a bird. You also have to think of the future, will you start being anxious even with a bird? Of course you know you and we don't know you. If you are getting a bird I would look for something smaller, a bigger bird might just cause more stress because sometimes they get agressive, just ask
@Shezbug. I think a tiel (they are sweet and like head scritches)would work for you, but if you meet a conure that fits your needs then you decide whether you can properly handle it. Remember they can sometimes bite hard and require some more care