If it is heat rash, you can monitor for the next few days and try cooling her and cleaning her. It will subside if it is heat rash. Over cny the weather was atrocious. So it could well be heat rash.
Is the skin around the dots rough? If it is rough, it could be an allergy. It could be anything from dustmites to something which you could have eaten and passed into your breastmilk to her. If it is, then you might want to try applying some moisturizer on those patches. I'm using Physiogel lotion. Some people I know also use California Baby Calendula cream. For really bad cases, doctors will prescribe a steroid cream. Try to remember what you ate over the last few days and avoid the new items which you've been eating to rule out food allergies.
If it is measles or chicken pox, your baby should be starting to run a fever already. If there is a fever, please bring your baby to see a doctor immediately.
Is there any other things that you notice that came with the dots? Like crankiness or diarrhea...
If it is mosquito bites, you can use Zambuk.