It depends on the Landlord-Tenant laws for Nevada. Sometimes when you separate a deposit by giving it different names, the deposit can only be used for that intended purpose and nothing else. That's why it is in your best interest to call all deposits a security deposit so damages and any outstanding amounts can be deducted from the security deposit with no problems.
Yes, you can sell your home. You will need to read your the contract you signed thoroughly to see if you are obligated to pay the management company any money for breaking the contract. You will have to check to see if the company is entitled to a flat fee regardless if your home is vacant or not or was their fee based on a percentage of the rent collected. Also, you will need to check to see if the contract has a "Buy-Out" clause that would allow you end the contract sooner, but keep in mind, even after all of this, you may be obligated to pay the amount that is still left on the contract.You should see if you can end the contract first with them as amicably as possible. Then check to see if they are willing to settle on a lesser amount. Hopefully, calmer heads will prevail without having to pursue legal action.
You have to keep in mind that you have lived at the Flamingo Apartments for eight years which most likely means you a month-to-month resident now. If that is the case, TLC Management can change any part of the lease agreement or add new rules or regulations by simply giving you a 30-Day Notice of Change in Terms of Tenancy, barring any state laws or local ordinances.