That must have been a tough loss for your family.
Look into the vital statistics acts in the area he was born in to find out how his birth and death would have been registered. Some jurisdictions have special registries for stillbirths, and as such their names don't appear in traditional birth or death registries. Some areas don't or didn't require registration at all.
Your brother's burial in a shared grave was not uncommon for infants until recently. Some cemeteries have common areas where stillborn babies and small infants were laid to rest without markers. Occasionally, infants were buried with adults who had died around the same time. Check the BMD to see what other deaths occurred around that time, and contact cemeteries in the area to see what they can tell you.