text message replication (undesired)

Greetings

I am unfamiliar with the use of devices that operate Android OS as I've  always used apple phones and devices. I am a  postpaid subscriber and recently my iphone was lost or stolen and there is no ATT or Apple stores in my area so I replaced it with a cheap android go phone I purchased at Wal-Mart, to use for a short time untilI have paid off the lost device and happen to be someplace near proper phone store sometime and have decided what it is I want to do with this account.  I don't want lose my phone number as I've had it since the 90's.  

I haven't been using this line very much and I think I had only sent and received a couple text in the couple weeks I've had the new phone.   A couple I were expecting never were received at all. Currently I primarily use this line at my home  and previous phones always had poor reception at my home but were always usable.  This one has trouble even keeping a network connection at all and all cellular voice and data service is virtually impossible and of such poor quality to render it useless. So I must rely on my home wifi and must keep calls forward to my home phone.

I sent a message to my physician the other day and I remember I had to hit retry once or twice before the phone indicated the message had been sent.  And the records in my phone only indicate just the one instance of this message being sent.  Yet my doctor said he received the same message over 100 times in a about a 3 day period spanning the weekend.

What could cause this?  Can I have messaging disabled as I'm not really using this phone much.   Albeit I am unfamiliar with the use of the android OS, I am however quite proficient with the use of electronics in general and do no believe this to be a user or hardware related issue.

Is it possible to block text messages all together on this line?  I'm afraid to sending more text messages until I'm certain this won't happened again so any ideas or suggestions as to the cause or as way to prevent this from happening in the future.  

Thanks for you help

Cheers