Vaccinations given in government are also at par with the private ones. Painless and normal vaccines have almost same efficacy. But not all vaccines are given by the government. Therefore u may take vaccines from govt, but u need to complete the vaccination schedule with a private practitioner as well.

Consult with Pediatrician physically for further evaluation and treatment

Both government and private sector vaccines have same efficacy. The only difference is of painful and painless vaccine because of acellular component of pertussis vaccine (available in private clinics), and also the painless vaccines are costly. If cost is not an issue then you should go for private clinic as it's painless. Try to stick to same brand as far as possible but if not available then you can get a different brand vaccination too at 10 and 14 weeks.

Government vaccines are good enough as they are providing most of the vaccines like penta , pneumo IPV and Rota free of cost. If you take these vaccines in a private set up, it costs a lot of money. Govt. is giving whole cell vaccine which causes fever, whereas in a private set up, you can take acellular vaccine, which is painless, however, the immune response of both the vaccines are almost similar. Government is not giving some vaccine like chickenpox, typhoid, hepatitis A influenza, which can be taken separately.