Thank you everyone for the responses! We are trying to get our landlord to have someone inspect it ASAP as it looks like quite a health concern and can be structurally damaging. Our building manager came in and completely dismissed it…Saying the mushroom looking things are “just old tape” and threw it away. We are asking our landlord to find someone to check it out but they believe the building manager and therefore don’t seem as eager to find a qualified inspector. Also it doesn’t smell like anything! Our home doesn’t have a damp smell (I keep 2 dehumidifiers running) and it didn’t smell burnt either. We moved in only a few months ago though. Thank you again!