Sounds like a traumatic ER experience, I had one of those myself once. Ugh.
Actually, I'm about to set up an appointment with a GP (once I locate one!) for blood tests for nutritional deficiencies and whatever else they might find... so, I'm gonna chime in and say you CAN do it!! I totally agree with the others that if you set up the appt, you will be more in control than that ER experience where you panicked. Also, you can mention up front to the doctor and nurses about your fear/anxiety... I'm sure they will try to be accommodating. Just let them know you have some anxiety in situations like this... it might help to get it off your chest before going in there for the actual tests.
Good luck! You got this!