Do you have online access to your blood test results etc? I can book appointments online through the same link although there isn't the same amount of choice online as on the phone.
Also is your fear of phones a phobia of the actual apparatus or of the person at the other end of the line? I sometimes struggle with telephone calls but am OK with automated phone appointments, I am OK with 'pressing 1 to accept or 2 to continue to hear available appointments' etc For me it's an extension of agoraphobia which personally comes down to a fear of people (which, like your phobia is down to events as a child.)
A lot of my blood tests are done at the hospital, which sends results to my GP by letter. The letter is then scanned in, but the actual numbers aren't transferred to the system. So if I want results from my GP I have to make an appointment to see my GP because only doctors can look at my detailed medical records. Unsurprisingly, I choose to get my results by letter and email from the hospital.
The surgery used to do prescriptions, appointments and general queries over the internet, but apparently COVID means they can't do this anymore. No estimated time of restart, either.
The phobia is probably both. I have vastly improved from when the telephone ring used to make me run and hide, but there's still no way I'm even touching a mobile phone.