Lightly bitten by puppy... should I get anti-rabies shots?

While I was walking home last night, my cousin's puppy playfully bit me on my shin. At first, I was not entirely sure if it pierced through since it didn't bleed yet the area was red. I washed it with soap and water as a precaution. Then, I applied hydrogen peroxide to see if my skin broke. There were 4 dots on a row that "bubbled" so I believe it confirms that my skin did break. 10 hours later and I'm worried about the possibility of having contracted rabies. Looking at the bite area now, there are no visible wounds so it makes me anxious that the doctors would just brush it off. The puppy was about 3-4 months old and have never been vaccinated against the virus. Please help!