You should stop riding this- now.
Assuming it is just loose cones/nuts on the axle, it is a 20-minute job to do the following:
- Remove the skewer (duh)
- Remove the cassette
- Loosen and remove the axle from the non-drive side
- Pull the 18 (more or less) ball bearings from both sides and clean out the bearing cavities
- Check for play in the freehub - you might as well tighten up the freehub while you are at it.
- Replace all of the balls with new: for all of a $2 cost for the balls and grease you may as replace all
- Check the hub cones for pitting/wear
- Properly tighten/lock up the drive side cones
- Reinsert the axle and properly adjust the non-drive side cones. Make sure they are locked-up against each other
- Reinstall cassette and properly tighten the lockring. As in do not reef on it until the tool explodes.
- Done
If you've messed up one of the cones, it is a $10 replacement part. Easy to find online. It takes an extraordinary amount of abuse to irreparably kill a Shimano hub.
If you are dealing with a bike shop on this fix, add 10 minutes of arguing prior to step 1 when they are trying to convince you that you need an entire new wheel. If they are not clear as to how to tackle this, print this list off and show to the shop guys.
Only wrinkle: you actually may have broken an axle on the drive side. This is incredibly rare. If so, add another 10 minutes to replace the axle. At our Co-op, we have 10 pound bin of axles and cones that we sell for basically nothing.