Your GP will make a judgement about your health as you describe how you are feeling. S/he will not insist that you take medication, although that might be suggested. There are numerous ways of dealing with anxiety, either in conjunction with, or rather than, medication, which the dr should be able to help you access, although sometimes the waiting list is quite long. If your employer pays into an occupational health scheme, it would be worth your asking for a referral to them. They can often get access to therapies which don’t have such long waiting lists. If you do get a OH referral, please take someone else with you to the appointment, If you are a union member, ask a rep to accompany you.
I’m another who thinks that you could profitably look for a different job. Your employer doesn’t sound very supportive.