Some dogs can have allergic reactions to cedar chips or walnut chips in bedding (there are a lot of dog beds that have this in them). If you have either of these remove them and see if the red spots go away on their own.
Some shampoos (especially any with pennyroyal) can cause an allergic response. Dry skin (especially in winter) can also cause red spots.
Food allergies are always a possibility, but usualy there is itching with this. It could also be a bacterial or yeast infection.. antibiotics usually clear this up in 3-4 weeks.
Contact dermatitis is always a possiblity (carpet cleaner, floor wax, etc) but usually there is itching with this as well. Check around areas where your dog is allowed to be.. if there is anything new that could be the problem. Remove the offending product and see if the rash subsides on it's own.
If the rash continues for a week.. or worsens at anytime.. you will need to take a trip to the vet for and exam. Skin scrapings will give a definitive diagnosis.
I hope this helps and she is better soon!