You can get a very inexpensive do-it-yourself mold testing kit online, test the mold and send it in for evaluation. You can then decide whether the mold is of concern or not, because there are so many. You should contact your landlord regardless, because he/she would want to address the moisture issue as soon as possible before it results in serious damage to their property (and you!).

If there is a serious mold issue and your landlord isn't prepared to address it fully and properly, you should move out. Be sure to wash all of your bedding very carefully and wipe down furnishings so you don't bring spores with you.

Thanks for the response. The problem is that there is no visible mold. I am trying to figure out if mold could possibly be inside the wall at this point. Someone also advised that mold can be around the windows, also not visible. I have lived here for 30 years and am trying to work with the landlord to resolve this. Thanks again.

I think the last person I'd call is a "certified mold inspector." I tend to trust people more when they don't have a stake in selling a remedy... whether I need it or not.
AC sounds like a window unit. Can't help wondering if maybe its not tilted/leveled properly to keep condensation outside. Could that chalky bulge be built up mineral deposits from condensation? Really don't know, just wondering if that could have happened.
Glad your landlord is working with you. Sandy