If the problem is heat stroke, you will also see greying around the mouth and tongue area. If you don't catch it soon enough, you can have permanent neurological damage.
The most common cause of these symptoms in animals is vestibular disease. It's a disease of the inner ear and it will cause staggering, falling over, one sided paralysis and the dogmight hold his head at an odd angle.
I suggest that you go to the vet immediately so that they can culture the ear and rule this out. If it is vestibular disease, your dog can be treated with strong, long term antibiotics.
Keep in mind that the effects of vestibular disease can clear up somewhat on their own and you can see some relief from the symptoms at times even without antibiotics. This does not mean that the disease has cleared up, it only means that the symptoms are not as prevalent.
If this progresses, there is a good chance that she will not recover from the symptoms even if you treat them so time is of the essence.
Let me know if you still have questions.