Help with HAP and letting agents

Ok... so sorry this is a long one and I hope it gets a decent response because I am at my wits end. I was approached by a letting agent after I was in the running for a property that I didn’t get. She showed me a property not yet on the market for myself and my son and honestly it was lovely. HAP didn’t seem to put her off. I’ve been approved in principle (as in I’m on the housing list). Anyway I’ve paid my deposit and first months rent and can afford to pay until HAP kicks in, possibly even longer as my earnings are ok. Anyway I was promised the keys today if I paid the first month (deposit is already paid) and came in to sign the lease early because of all this covid crap. Anyway after I did all that she told me she wasn’t going to give me the keys until I was approved for HAP despite knowing I can pay. She also knows I only have 3 weeks left on my lease. The lease I signed today is for the 1st of Nov. I’m currently sending in her half of the application when I told her I already sent my part in in an email. She keeps chopping and changing and doesn’t listen to me. I want the house but now I’ve given her the only chance I have of getting a gaff as my lease is up where I am. She also wanted me to register for bills before I moved in but I don’t want to as I don’t live there yet. I know HAP applications are taking a while at the moment but I’m prepared and able to pay for at least 3 months. What should I do? Is there any way to get proof from HAP once I’m approved or what should I do? I’m scared she won’t give me my money back. I literally burst into tears