My question involves labor and employment law for the state of: Texas

I worked for a company for 13 months. This past Sunday, I received a call from one of the owners, yelling and telling me I was fired. I was then called in by the HR manager, who asked that I come in to the office. I told her I would and about 3 hours later, arrived. She was there, along with my immediate supervisor. They then accused me of having a personal relationship with the first owner's wife. They stated they had proof, in the form of text, email, and voice messages. I was completely shocked, denied it, and asked to see the proof; they denied. They then said I could either resign (and stated the positives of this, mainly referrals), or they would fire me. I chose to resign - hindsight, I should have done nothing... I was just totally caught off guard. I wrote on a blank paper my resignation, dated and signed it.

Today I went in to get my final paycheck, and sign a form that I had turned in all company-owned equipment, credit cards, etc. I asked that they allow me to rescind my resignation so that I could collect unemployment, they refused. They gave me a stack of paper, with COBRA information, and a hand written copy of the equipment form. They also handed me the original, signed, in my writing, document I wrote on Sunday, stating my resignation! I could not believe this.

My question is - did they make a copy of that and if so, is that valid? If not, is it true I did not resign?

Thank you to all who respond.