Summarize:

Go to https://www.facebook.com/. This will open your News Feed if you're already logged into Facebook.  If you aren't logged in, enter your email address and password in the top-right side of the page before continuing. This method only works if you or the person whom you suspect blocked you had at least a one-message conversation with each other. You'll need to use the Facebook website version of Messenger, since the mobile app occasionally still shows blocked accounts. It's a speech bubble-shaped icon with a lightning bolt in it. You'll find this in the top-right side of the page. Clicking it prompts a drop-down menu. This link is at the very bottom of the drop-down menu. Doing so opens the Messenger page. Click the conversation with the person whom you think blocked you. You'll find it in the left-hand column of conversations. You may have to scroll down through this column to find the conversation. It's in the upper-right side of the conversation window. Clicking it prompts a pop-out window to appear on the right side of the conversation. If you can't find a link in the sidebar below the "Facebook Profile" heading, you know that they did one of the following:   They blocked you. When someone blocks you, you can't reply to their messages or visit their profile.  They deleted their account. Unfortunately, the exact same thing happens when someone deletes their account.
Open Facebook's website. Click the Messages icon. Click See All in Messenger. Select the conversation. Click ⓘ. Look for a link to their profile.