I can't receive nor text message to one person and vice versa. We both have iPhones and this is a recent problem this past week.

What OS are you operating?

If you open the Settings app on your iPhone, select Messages, and set the iMessage slider to the off position, you will no longer send or receive iMessages on the iPhone. However, depending on your situation, you may end up not receiving text messages from iPhone users. Additionally, if you have multiple Apple devices, the iMessages will still be delivered to your other devices. This is usually not desirable because you want messages sent to your phone number to be delivered to your iPhone.

Check this link for details:

Why Am Not Receiving Text Messages From iPhone Users iAnswerGuy

You can block text messages via Messages app. This works really well for blocking text messages on iPhone, like some unknown spammers, advertising companies and internet marketers bothering you with promotions and offers for products that are not at all related to your interest. These steps will block only those unknown callers that you choose to block.
1. Go to the Messages app.
2. Tap on the target message from the spammer.
3. Choose "Details" on the top right hand corner and tap on it.
4. There will be phone icon and a letter "i" icon across from the number. Tap on the "i" icon.

5. Scroll down to the bottom of the page and then tap on "Block Contact".
Note: Once you press on Block Contact, the phone number that you just blocked won't be able to make phone calls, send text messages, or Facetime you.

How to Block Text Messages on iPhone

make sure you have the correcct time and date set on the iphone.
Good luck.

when sending messages, check the top of the create message screen that there is only one contact listed in the "To" boxes

Copy and paste into a new message.
Put your finger on the message you would like to forward. Select copy. Open a new message window. Choose the person or persons you want to send the message to. Place your finger where you enter the text and choose paste. Then send.

first thing i would do is to make sure you have the area code included in the contact entry.....this is most like the problem

If you connect your phone to your computer using the included USB cable, you should be able to search any files that are on your sim card, memory card, or phone. Also, there should be an option on your phone whether you would like to save your text messages to your sim card, memory card, or phone. Just like a picture, ring tone, or song. Hope this helps.