My son's BCG also looked like an acne (with pus) when he's 2 months. We didn't touch it. Close to 3 months, the BCG sort of burst and got discharge and some blood. Asked the pediatrician, she said so long as the BCG doesn't grow in size then is ok. She said coz the baby is still developing immunity.
Recently got some more blood, will check with my pediatrician during his 4 month injection. If you are worried, better check.