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Unfortunately, most convensional lender wont lend less than 45k. I would recommend you to contact a private lender. They will able to help you with the down payment you are putting down.
Some sellers might offer you seller financing with so much down payment.
Your problem is going to be finding a home in that range. Preston Hollow is a bit more expensive than $30k. Only some townhouses on the west side are down in that range and they have $200/month dues. Most single family homes in Preston Hollow are in the $300-999k range, with some in the $250-300 range.
We can help you. We're a private money lender and have a NO DOC loan program that's not credit score based. We require 35% down and don't care about the condition of the home, so long as it appraises equal to the purchase price on the contract. Please give me a call or send me an email and we can discuss your situation and next steps.