How do I check if coolant is really going into the oil

Coolant in the oil will show up on the dip stick looking like a thin chocolate shake.
If it has been setting a while the coolant could have separated out and settled on the bottom. The easy way to discover that is to drain the oil. The water will come out first. If the engine does have coolant in the oil and it stays in it, the coolant will damage the bearings.
It would be best to drain the oil as it is setting now, do not start it up. You could even drain it out and put some in a clear glass jar, the coolant will settle on the bottom.