Reconstituted rabies vaccine is fine for 6-8 hours at room temperature as long as it was never frozen or left in direct sun, so a 3-hour gap after mixing does not kill the potency. Your doses are valid and there is no need to restart the series - restarting is the commonest unnecessary panic I see. Complete the schedule on time and you are covered.
Next Steps
Just take the remaining doses on day 14 and day 28 as per your schedule, and keep the card safely. Wash the scratch site with soap and water even now if it is unhealed, and watch for redness, pus or swelling which would need antibiotics. If you want reassurance about the storage issue or a written record, book a Practo consult with me.