Freewheel or sprockets?
You may need to clean up your terminology to make the question more clear.  There are two common setups a freewheel OR a freehub and cassette.  The answer will vary greatly depending on which setup you have.  If you have a freewheel both items (gears and free mechanism) are one item and essentially you should just replace the freewheel and you would be done.

If you have a freehub (free mechanism is built into the hub which is more common/modern) you will need to determine if the issue is the hub or cassette and replace accordingly.

If you do have a freehub|cassette setup, I would lean (based on your description) to having a damaged freehub which you have likely damaged more by continuing to ride (based on your increasingly description).  Depending on the price of your wheel, you may choose to replace the whole wheel, rebuild the wheel with a new hub, or find a way to fix the freehub (possible if the hub body itself is not damaged AND it is an expensive hub).