Typical strep throat is an acute pain in the throat (my past experiences of Strep multiple times in one year). Not being able to turn her head or smile is concerning. If she says it hurts in her throat to do that, well, that might just be her sensitivity.
But if her other muscles hurt when she tries, it could be symptomatic of something more severe; a stiff neck is one of the accompanying signs of meningitis (rare). Or, it could be a very strong case of strep throat & inflammation of the lymph nodes (more likely).
Either way, a call to the doctor is definitely warranted. It may be that your daughter needs something for the pain until the antibiotics are able to address the infection. Or she may need a stronger antibiotic - 72 hours is plenty of time for it to have starte to take noticeable effect, & amoxicillin is only one antibiotic that can be prescribed.
So, if you haven't already, make sure to call your doctors office today. Ask to speak with the nurse (don't just leave a message with the receptionist for the doctor to call you, they are busy & a nurse can help make a judgement call to interrupt the doctor to consult, or advise you if you need to come in).
In the meantime, I'll just offer my one go-to food when I have a sore throat: Extra soft & creamy mashed potatoes with plenty of salt. McDonalds french fries work great too... The salt soothes, & the potato is soft enough to not scratch the throat.
Hope she is on the mend soon! T.