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I will try to best answer your question.
You need to get to a doctor immediately and get a note indicating that you have pneumonia and are medically unable to attend the hearing on Monday. You will then need to contact the court and fax the doctor's note immediately along with a written request for a continuance.
Based upon your facts stated you have a very strong custody case, but if you are not there to present these facts the court is only going to hear mother's version of events.
In addition since the child has lived with you for 2 years, you can attempt to change the jurisdiction from Texas to Tennessee where you are residing. Custody jurisdiction is established under the uniform child custody jurisdiction and Enforcement Act (UCCJEA). It states between two different US states custody should be heard where the child has resided during the last 6 months. I would think strategically it would be very important to try to change the jurisdiction to Tennessee so it is easy for you to attend court hearings and difficult for mother.
Handling an interstate custody case in arguing over jurisdiction correctly is not easy, I would highly recommend hire an attorney as soon as you are you able to do so.
I hope that this information and advice is helpful and I wish you the best of luck obtaining the continuance.