That's a bad idea in any case. And it sounds as if Marco is familiar with Texas regulations that would prevent you from doing that.
If the house is free and clear, then get a home equity loan or home equity line of credit. Then use that credit line or loan to expand your home. Another option--not as good as a HELOC or home equity loan--is to find a contractor who will arrange financing.
As others note, the tax value doesn't mean a thing.
And no hard money lender would lend to you for that purpose, anyway. Hard money loans are made to investors, not for primary residences.
So: Consider a HELOC or home equity line of credit. Failing that, find a contractor who offers (or can arrange) financing. Forget hard money loans.
Oh, and check with a Realtor to make sure that adding on to your house would return more than the cost at time of sale. Considering the hassle, expenses, etc., you should be looking at a return of 1.5 (for instance, if you spend $10,000, you should be able to sell your home for $15,000 more) on any construction or improvements you do.
Hope that helps.