Can't you send messages on Messenger to a friend of yours? This could be because it blocked your messages. Although Facebook allows its users to hide their information for privacy reasons, you can still tell if your messages have been blocked by looking for certain errors.
Steps
Method 1 of 2: Find out if your messages are blocked on a smartphone or tablet

Step 1. Open the Facebook Messenger app
The app icon looks like a blue bubble around a white lightning bolt. You can find it in the app drawer (if you're using an Android device) or on the home screen.
Blocking messages on Messenger isn't done the way you do on Facebook. When someone blocks your messages on Messenger, you will always remain friends on Facebook and you can chat with them for a certain period of time. Besides, it can unblock you at any time

Step 2. Enter the person's name in the search box
You will find this area at the top of the screen. Once done, you will see a list of names that match what you entered.

Step 3. Tap the person's name in the search results
Thus, you will open a conversation with this person.

Step 4. Enter a message in the input field
The input field is located at the bottom of the conversation.

Step 5. Tap the icon that represents Send
This icon is represented by a paper airplane. After this action if you see a popup window appear which notifies you This person is not available at the moment, know that he has either totally blocked you on Facebook, has blocked your messages or has deactivated his Facebook account.
If the message passes without error, all your messages will reach your recipient. The latter may not have connected to read them

Step 6. Find out if your friend has blocked you or deactivated their account
If you had received the error message, the last thing for you to do would be to find out if their profile (the one displayed on Messenger) is different from the one displayed on Facebook.
- Open the Facebook app. The app icon is represented by a white “f” which you can see on your home screen. After that, search for the person's name. If you can't find her profile, she probably deactivated her account or blocked it completely. But if you notice that her profile is the same as the one that appears on Messenger, know that she has only blocked your messages.
- If you can't see the profile, ask a friend you have to check it out for you. This is the only way you can tell if you have been completely blocked. If your friend (the one you have in common) happens to see the profile and you don't, know that you have been blocked by the person.
Method 2 of 2: Find out if your messages are blocked on Messenger from a computer

Step 1. Go to Messenger
You can use any browser to access Messenger on your computer.
Blocking messages on Messenger isn't done the way you do on Facebook. When someone blocks your messages on Messenger, you will always remain friends on Facebook and you can chat with them for a certain period of time. Besides, it can unblock you at any time

Step 2. Access your account
If it's already done, you'll see a list showing your recent conversations. Otherwise, click on Continue as (your username) or enter your login information as requested.

Step 3. Enter the person's name in the search box
You can find this area in the upper left corner of your screen. As you enter the name, a list of contacts will appear.

Step 4. Click the person's name in the search results
Thus, you will open a conversation with this person.

Step 5. Enter a message in the input field
This field is located at the bottom of the screen.

Step 6. Click Enter Or on Return.
After this action, if you see in the dialog box (where you just typed) the following notification This person is not available at the moment, know that they have either totally blocked you on Facebook, blocked your messages or has deactivated his Facebook account.
If the message passes without error, all your messages will reach the recipient. The latter may not have connected to read them

Step 7. Find out if your friend has blocked you or deactivated their account
If you received the error message, the last thing you need to do is find out if their profile (the one displayed on Messenger) is different from the one displayed on Facebook.
- Go to Facebook, then search for your friend's profile. If you can't see their profile, they've probably deactivated their account or blocked it altogether. But if you notice that his profile is the same as the one displayed on Messenger, know that he has only blocked your messages.
- If you can't see the profile, ask a friend you have to check it out for you. This is the only way you can tell if you have been completely blocked. If your friend (the one you have in common) happens to see the profile and you don't, know that you have been blocked by the person.