You cannot take your son with you.
If the appointment is not until next Thursday, you have time to organise.
Call the clinic first thing on Monday, explain, and ask for an appointment after school drop-off. If you can't get through to the clinic, keep calling, and try going through all other avenues to find a direct line: google for alternative numbers, hospital main switchboard, your GP etc. Search for an email address for them. Do you have the NHS app, and does it come up as appointment on there? You may be able to re-book through the app.
If you really can't get the appointment changed, find someone - anyone - to take your DC to school instead.
When I was referred to the breast clinic after a mammogram, I couldn't make the day of the appointment they gave me, so I called to rebook for a few days later. When I turned up on the new date, they had no record of my new appointment in the system (NHS computer systems...), but they fitted me in anyway.
Within an hour or so I had had another mammogram, an ultrasound, a biopsy, and had been told it was almost certainly breast cancer, so they booked me an appointment with a surgeon for when the biopsy results would be through.
If you are lucky, your appointment will go differently, but there is no way on earthg that you could leave a nine-year-old sitting in the waiting room while you go through the process. I am pretty sure that clinic letters usually specifically say that you must not bring children with you.