Have you seen her do anything that could have made her arm hurt?
Ds does the huge sleep with tonsillitis, but if you wake him he knows who I am and isn't disorientated. He does this even now and he's 8yo and hasn't slept in the day since he was 3yo.
When she looks at you, does she know you, focus on your face, say something that makes sense?
Go and wake her, ask her a question. Like would she like a drink? Or Would you like mummy to get something. She needs to respond having understood the question. If she does she's probably just sleeping a bug off. If she's not really waking enough for that, then I'd probably go for the forced wake. For mine taking them outside (bright and cold) was always enough for that, then you can have a little conversation and feel reassured.
Will the GP not see you if you say it's urgent and for a child? Ours always will. The thing is with a child it's either quick, or they really need to be seen, so they don't mind. I last did it last Friday. You may need to explain to the receptionists that it is urgent, but they always have seen me when I say it is.
If she's not disturbing for that then if the GP hasn't phoned back, then it probably is a take to A&E check. Probably fine, but worth checking.
Ds once didn't disturb. I had popped him in the buggy (aged 5 or 6) to take the girls to an after school thing. Half an hour's walk, wait around an hour, come back, and he hardly moved in that time. Met the GP coming out of surgery and spoke to him and the conclusion was that ds was just sleeping off the bug. Sure enough the next day he was right as rain.