Infidelity Husband

Texas is considered a no-fault divorce state. This means that you don't have to allege a reason for wanting or needing the divorce.... you can just say you want out and the judge can grant the divorce.  Some states still require the parties to allege a reason like cruelty, adultery, etc... but that is not required in Texas.  So... most people don't allege a specific reason like adultery. 
However, those that do include a fault in failure of the marriage, like adultery, do so because they want the court to award them a larger share of the community estate.  Unfortunately, because adultery is so much more common than it used to be, many judges don't give huge awards even if the offending spouse admits the affair.  Some will give a slight bump, but it's not the windfall it used to be. 
The exception, however, is if he offending spouse depleated the community assets by giving excessive gifts to the boyfriend or girlfriend.  Judges tend to frown on spouses who basically defaud the other spouse by making excessive gifts to their paramours.  To have a better idea of what your judge would do.... you really need to visit with a local attorney.  Even though every judge is required to follow the Texas Family Code, the code is subject to a wide variety of interpretations which often results in a variety of approaches.
You ask, 'what should I do?'  What you should do and can do are two different things.  If you cannot accept that your husband had an affair, you can file for divorce, but you are not required to do so.  If you want to give your marriage a second chance you can.  However, if you continue to stay married to your husband after the affair, then the affair will have a lower effect on the judge should you decide to file later... mainly, because the judge will deem you a willing participant to the marriage and any accompanying problems of the marriage.
If you decide to file, you need to start documenting the assets and debts.  You and he can sit down and work out a deal of who gets what or who pays what.  If you cannot agree, then you will have to set the case for a hearing in front of the judge and the judge will decide who gets and pays what.  Many people leave a house, file for divorce, and then are frustrated because they loose access to their financial records.  Make copies before you leave... so you don't have to stress after you leave chasing it down. 
For property division, Texas uses a fair and equitable standard.  The judges will try to divide everything 'close' to fifty-fifty.... but the division does not have to be exact.  So, as you and your husband negotiate, shoot to make a agreement that divides the community estate in this manner.  Divorce usually means financial hardships because you are converting from a dual income household to a single income household.  A good goal of any negotiation should be to help the community estate. For example, if there are $10k worth of assets and $5k in debt.... you and your husband should consider liquidating some of the assets, paying off the debts, and dividing the remaining assets.  This gives each party the opportunity to start over debt free. 
The fact that you don't have kids basically makes your potential divorce a math problem.  The decision to have children is extremely personal.... but I would encourage you to hold off having any children until you and your husband have resolved your issues.  The most expensive and emotionally taxing divorces almost always involve children.  You do not need to add this layer of stress if you think a divorce is a real possibility.
This is a thumbnail of what applies in every jurisdiction in Texas.  To get a more specific idea of what a judge in your county may or may not do, I recommend that you arrange for a consultation with a couple of local attorneys.  They can give you a better pulse of what to expect from the local judges.