Yes, a relatively short exposure to concrete dust could cause your cough. This cough could be from the dust causing lung inflammation. After months or years this can become permanent. Despite what seems to be a good barrier, the wood dust could also cause the same problem. If possible stay away from your studio for 4 to 7 days. If your cough either lessens or completely goes away this is a clue that the dust is causing your cough.
In most cases, testing the dust would not be helpful. What you will need is an air conditioner that will filter out the dust.
I was recently exposed to concrete dust from our neighbor new inground pool. Was taken to the emergency room 4 times in 1 week. Symptoms: After lying down to go to sleep at night I would wake up already coughing and then my windpipe would close to a pinhole, I would gag and then be taken to ER. The first three times they could not find anyting on the xrays, so they treated as a virus. Didn't work. Couple days later, I had same episode, went to different hospital, diagnosed with Acute Tracheaitis, treated with prednisone and hydrocodone....worked! I decided to do my own internet research on the mucous build up on my vocal cords and why I couldn't expel it. Found something called Vocal Cord Dysfunction....do not know if that is what it is, but I am pursuing all I can to nail this thing. I ran out of the hydrocodone, which not only is a pain killer, which I had none, but it also helps in breathing tremendously. My throat feels as if there is a knife pricking at it when I try to clear it, I have learned to relax my breathing when I start to cough, although sometimes it still gets the best of me and I start to gag again. From the MSDS's I've read on concrete dust, it doesn't look very good, but new technology is always coming out, let's keep our hopes up.