Bidding war - Binding email acceptance?

[Dan Jung]

In Florida, I've offered and been counterofferred on a bank owned REO via email exchange through a realtor. I accepted the bank's counteroffer with email. The realtor said there were 2 other offers that she was obligated to send to the bank. I accepted the counteroffer before the other offers were tendered. From my rudimentary understanding of contract law, don't we already have a binding contract that is "signed" over email? If the bank accepts and goes to contract with another party's offer, do I have any legal recourse?

Thanks in advance.