The experience of "milk coming in" can vary from person to person, but it's generally not painful.
The feeling is often described as fullness, tingling, or pressure in the breasts. This is due to the increased blood flow and milk production that happens after giving birth.
Some women may experience mild discomfort or soreness, but this is usually temporary and resolves on its own.
If you're experiencing severe pain or discomfort, it's important to contact your doctor or healthcare provider. They can help determine the cause and recommend appropriate treatment.