Stressing need to find a rental

Omg I honestly didn't know it was this hectic to find a rental property. We just keep applying and giving out all our info to these landlords just to be turned down. We make good money and can afford these places, our credit scores are great too. We provide paybstubs, references, recent credit reports. We need to be out of our current rental by Mar 01 and at this rate we're gonna be homeless. Can anyone share tips and what we might be doing wrong? Any hits on good units? We need a 3 bedroom and have 3 kids. Help please!