Thanks for the question.
The issue here is typically the tilt pins. The pins can come loose or wear out and cause your issue. They should be replaced.
Here is a picture of the location on the sides of the column.
Sorry the picture did not come through for you. Here it is again, it should work this time.
The pins actually just tap in. They come out from the sides of the column, not from the inside. If the pins are really tight, then a special tool, like in the picture, will be needed.
There is a chance that a part store will have them, if not I am sure they might be able to order them, or you could check a GM dealer. I did check AutoZone, and they do not have them. I would have it fixed as soon as possible to help prevent anything else from happening. Basically, if those pins fall out, then the only thing left holding wheel on the column is the tilt spring, which is not good.
If I remember correctly, if you tilt the wheel all the way up, you should be able to see them both. The cover may hide a small edge, but they should come out that way. That is how I always did it.
Then yeah, you will need to pull the housing, which can be difficult, as a special tool for the lock plate is needed to release the plate.
If you have an airbag system, then the SRS coil will have to come out, it is held on by a C-clip, then the lock plate is behind that. The plate will need to be depressed using the lock plate tool, and then remove the C-clip holding that plate on. Under the plate, you will have to remove a few screws holdig the rest of the turn signal assembly in place, a torx head screw holding the lock cylinder in, then a few more screws holding the housing on. It is really not that bad, just a lot of stuff has to come off in order to remove the housing.
If you have any other questions about it, let me know.
The one talking about the u-joint think the steering shaft has come loose, which I do not think is your case, else you would not be able to turn the tires. The GM dealer talking about the 3 bolts may be talking about the column mount, but if that was the case, the entire column, top to bottom would be moving around. The one that said they have the pins sounds like they know what you mean. When the pins fail, the top part of the column, after the tilt, will move all over the place and the lower part will be ok, and the wheel would still turn, so I think it is ok to be confused there for a moment, since a few people all gave you different answers.
Hopefully this cleared that up for you. Go with the store that said they have the pins.
Your welcome and thank you.