No, it's absolutely not .
You did the best thing to get a vaccine, continue with the regime.
Next Steps
Get your wound examined.
Health Tips
For future reference.
in case of any animal bite
1- clean the wound with soap and water.
2- Do not use antiseptic solutions like Dettol before washing the bite area with soap and water.
3 - Do not do dressing of the wound, keep it open.