The symptoms of hypothyroid and hyperthyroid frequently cross over. For example, anxiety appears on both lists. And either one of the thyroid disease can cause problems with the hypothalamus in the brain, which regulates temperature. This dysfunction doesn't appear the same for each hyper- or hypo- person... That is, not all hypos are cold and not all hypers are hot. They can be either. That's why a diagnosis can't be made by symptoms alone. At some point, you're going to have to have bloodwork done.
Your phobia might even be driven by the thyroid disorder. I don't know what to suggest to get you around that Catch 22, though. I know that appealing to reason doesn't generally work when it's a genuine phobia, so that my telling you it will be ok isn't going to help. Do you have a close friend, relative, or spouse whom you can get to help you through the diagnostic process of bloodwork and seeing the doc?
The thing is, if you're hypoT, you can live a long - probably miserable - life before it kills you. But if you're hyperT, it can be more immediately life-threatening not to treat it. You really must find out what's going on with you ASAP.
I have found most medical support people to be extremely compassionate and caring. [Doctors themselves have been another story, but I digress.
] If you're upfront at the beginning and let them know how nervous you are about having blood drawn, they'll do their best to ease you through it. Don't be embarrassed to admit your discomfort; lots of people have the same fears. I'd bet lab techs see it every single day.