Every marriage in Texas is presumed valid. (Texas Family Code section 1.101 and 1.102) To overcome that presumption, one would have to show by clear and convincing evidence that there is some impediment to validity. In this case, his wife was an impediment to your marriage being valid. However, as soon as the impediment is removed, the marriage becomes valid as of the date the impediment is removed. In your case, the impediment was removed on the day his other wife died. Your marriage became valid on that date. (Texas Family Code section 6.202(b)).
During the time that the previous wife was alive, you would not have accumulated any community property, which will be an issue (a) when he dies (if there are kids from the prior marriage and he does not have a Will); or (b) if the two of you ever get divorced.
To clearly answer the question, you cannot marry a second person while you are already married to a first person. So, technically, no, he could not have married you the first time regardless of the tragic loss of his first wife. You must, therefore, if you decide, marry again to have a legally binding marriage.
This is just an opinion, and is no way to take the place of an attorney that knows all the facts of the case. Therefore, I would seek such advice as soon as possible.
There was an impediment to your marriage, namely, your husband was already married. So your marriage was invalid so long as the impediment existed. Once your husband's wife passed away, the impediment was removed and you are, more than likely, common law married in the State of Texas. In order to be certain, check with a family law attorney in your area and you can file notice of common law marriage with the county clerk. The common law marriage would have begun after the death of your husband's wife; because, as previously stated, no one can be married to two people in the State of Texas, only the first would be legal.