The answer is not clear based on your facts. You can either have a holographic Will (which is what is sounds like the intent was), or an attested Will, which would normally require 2 witnesses. It is not clear if you had two witnesses or not. If not, it might not nullify the holographic Will to have a witness, but having a witness is not required. I would have this reviewed by a lawyer to determine what the effect of the document is.
You are almost certainly going to have this Will challenged, if it cuts off beneficiaries/devisees from the first Will. Since you will need to have a lawyer assist you in defending the Will, you might as well meet someone now, to help figure out where you stand.
I am licensed to practice law in the State of Michigan and have offices in Wayne and Ingham Counties. My practice is focused in the areas of estate planning and probate administration.
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You would be best-served by talking to a Texas licensed attorney. Some states recognize holgraphic wills (hand written) if they are attested to (witnessed). Usually two disinterested witnesses are required. In certain situations, in some states, the holographic will doesn't need to be witnessed (for example, in Maryland if its a soldier in combat, and then there are still limitations). Because of the variations state by state it's important to focus on what the law is in Texas.