How can I get rid of musty damp awful smell in carpet and air in room

concrete wicks moisture,take out carpet and tile it after sealing the concrete.

It sounds more to my amateur ears based on my experienced nose that the glue or other adhesive used to put down the flooring or wall covering may be the culprit. The heat of summer would activate the odor, which would wear off with enough ventilation.

Unfortunately, another reason could be the new wall you built, any seams around Windows, a leak in the roof that has not come through the ceiling, or even wet ground under the flooring (especially if you are using the cement floor without a new subfloor), may be causing the odor. This could be unhealthy, so using a ceiling fan and deodorizers will not help.

Do you have a contractor who is a friend who could check it out for you? With so many options, you may need a professional opinion. Best wishes 😇

You have an excess moisture problem. Have you tried a dehumidifier?

Once mold/mildew gets in rug it is also in the padding. Since mold/mildew is a very dangerous health hazard; remove rug & padding & scrub floor with a mildewcide. Sounds like a hi humidity area caused by the cement floor, which sucks moisture from under it & exhausts into the room, keeping the flooring humid. Best & healthiest solution: Toss out (or use as landscape cloth as I do) carpet & padding,then paint with a moisture block surface coating & use a renewable floor finish product. The ONLY 2 choices I can professionally recommend is "Cork" It looks just like hardwood & comes in several woods: oak,pine,walnut, etc. Cork is quiet, warm, soft, & short of dropping an old fasioned TV from the ceiling is just about indestructible. The other is "Bamboo" and the description is the same as for "Cork" and both are made for the "weekend warrior" to easily install. Just follow the directions to a "T"

I bought an ozone machine on line for less than $70 for a musty garage smell that was getting into the cars. My unit could run 2 hours ..... the odor is gone! (I assume there is rain water getting in under my doors but this was easy.) Don't breathe ozone .....let it air before using the room.

Probably have moisture wicking up through the cement pad, what flooring did you put down and what kind of barrier/pad did you use? Did you seal the concrete first?

Did you put insulation in the walls? Could be mildew or mold forming, I would dry it out with a heater on low and dehumidifer first. Open the windows and put a box fan in it to exhaust the stale air. I would also use Room Shocker. https://www.amazon.com/s/?ie=UTF8&keywords=room+shocker&tag=googhydr-20&index=aps&hvadid=181869104355&hvpos=1t1&hvnetw=g&hvrand=1207279987860734309&hvpone=&hvptwo=&hvqmt=e&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9033057&hvtargid=kwd-10706005469&ref=pd_sl_8yzwox9nhf_e_p19

This is likely from the moisture that the wooden floors have. Lift up a corner of the carpet, and see if you can lift more carpet up to see what the real problem is. There maybe a leak under the floor, and you are getting a spray from the water pipe under the floor. Have a skilled person check this out for you. Best wishes, J.