I applied for an apartment and was approved I paid my security deposit and have to be out of my current residence in 3 days the apartments told me I could move in this week I called them do get a official move in date and now they tell me all the apartments are rented. What can I do? Do you think this is a good Fair Housing Act complaint?

Why are all the apartments rented, is one going to be empty just not empty yet, did a renter refuse to move ?

Why are they not letting you move in. Did they rent to someone else, did they give you the money back, did you fail to do something?

If they are not going to let you move in because of a protected reason, race, religion, family situation, disability, then you have a complaint

If you now have additional costs and there was no fault of your own, you may have a law suit for those costs.

But honestly I would worry about that next week, today I would find a new apartment

I applied for an apartment and was approved I paid my security deposit and ...the apartments told me I could move in this week ...

Did you and the landlord which approved you both sign a lease?