You won't get this arrangement - of a guaranteed twice weekly arrangement - anywhere else. How did you get your gp to offer this?!!
the receptionist was following the instruction that you can only be seen by one GP that has made this arrangement which is reasonable given you already go twice a week.
Since you are wanting to go more often it is understandably unique situation that you should clarify on Thursday. You said that you felt you could be seen if urgent but I doubt this was your practice opinion. The receptionist has been told you were to see only one doctor and they are away. Just clarify when you see your doctor again.
Nhs 111 is a terrible service for hypochondriac - you call for reassurance but you will get told go to a&e or urgent gp appointment for everything else - not the reassurance you need, particular with anxiety disorders.
Best of luck x