I have recently began a basement remodeling project. Metal studs from cement floor to ceiling joists, greenboard on the walls. The ceiling has been furred down across the floor joists for a tongue and groove ceiling . I used 2x3s for furring as I needed to get down from the floor joists 1.50 inches to clear a couple of pipes. The 2x3s are 16 in on center and all shimmed for level. Now here is my problem . My floor upstairs seems very creaky now and lumps are appearing under the carpet in various places my guess is that nails are working there way up but unless I strip back the carpet I am unsure. What could be possibly going wrong here ? And more importantly how should I address the problem. Also I live in NY the home is a ranch and is 11 years old.

Was everything fine before you started the basement work? Perhaps the vibration from hammering the 2x3's has popped a few nails. Most carpenters today would use screws on a floor to avoid this problem. 11 years ago, they should have at least used flooring nails (with the ribs on them). Perhaps they just used regular nails.

I think you've got a few 'brute force' options
1) hit the nail heads down as best you can through the carpet... without ruining the carpet. (Be careful!). Now that the basement hammering is finished, maybe you'll be lucky and not have the heads reappear.
2) roll the carpet up, pull up nails you find and replace with screws. If that does not solve the squeaking problem then use more screws. This will be more work - you'll have to rent a kicker to reinstall the carpet etc.