Sounds to me like your water pump might be leaking which might or might not be the same issue as what the “mechanic “ found. I say that because he should have given you a little more information on exactly what kind of coolant leak he found- is it external or internal where it would be mixing with coolant and giving you milkshake oil. Another thing to note is although rare, sometimes the radiators fail and depending on options, you could have coolers for engine and transmission oil inside the radiator. If those coolers leak internal of the radiator, you can get trans fluid or motor oil mixing with engine coolant. It’s rare but it can happen. Have you checked your oil to see if coolant is mixing with it?