There's actually no negative effect though BCG is usually the first injection given to newborns as you've been told, just that baby is not protected from TB infection which is very risky.
In this case, you have to keep baby away from visitors/adults that can infect the baby.

Hello Ma'am, No. It does not have any adverse effect. No side effects, It is the place for easy identification of the scar.

Do not burst it ma, the pus and swell are normal signs of BCG vaccination when given to a baby, Yes ma, please leave alone, it will resolve on it own

you don't have to worry about this. A normal reaction to the BCG Vaccine. If it ruptures, take him to the hospital. The doctor will know what to do.