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I'm sorry to hear about your situation. There are "fault based" reasons for divorce in Texas, but this would not apply. Fault-based grounds for divorce include cruelty, adultery, conviction of a felony, abandonment, living apart for at least three years, and confinement to a mental hospital. In a no-fault divorce, however, the court will not assign blame to either party for the divorce. Adultery requires actual showing of proof of adultery (sex) and not just "emotional adultery".
Now you can file for a "no fault" based divorce, and the court can still consider any relevant factor in determining custody, distribution of assets, etc... But unless you can show actual adultery, you can't use that as the "fault" for the divorce filing.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!