It's possible that you have a blown head gasket or a cracked cylinder head if you pour water into the radiator and it ends up in the oil pan of your 2001 Blazer. Coolant and oil should never mix because the head gasket provides a seal between the engine block and the cylinder heads to keep these two fluids separate. When the head gasket fails, coolant can leak into the combustion chambers and mix with the oil, resulting in your symptoms.
It's important to have a qualified mechanic inspect your vehicle to confirm the exact cause of the issue and recommend the appropriate repairs. Driving with a blown head gasket or cracked cylinder head can lead to further engine damage and be hazardous, so it's crucial to address the problem promptly.