If a bone into sinus was broken and you blew your nose because your doctor didn't tell you about it, can the fragment of bones be lodged in the brain?

Possible: There are sinuses separated from brain by a bone wall. It is possible that if the bone is fractured, the brain may be involved. So, the answer is which sinus had the fracture is important for an accurate answer.

Extremely unlikely: If a nasal fracture occurred that could form bone fragments that could go into the brain, the initial injury would have had to have been so traumatic that you would have been hospitalized and severely injured. At the time scans would have picked up any bone fragments that could have been problematic.