In the same boat as you, glad to know I'm not alone. Tried a few things, nothing seemed to work; Rebooted computer, turned off anti-virus, reinstalled Minecraft, reinstalled Java. No luck. Server is up, few people on it right now.
Now this fix may no be the problem for you, but its quite likely.
I remembered adding a line to my hosts file to fix a problem I was having connecting to servers a while ago.
So in order to do this you have to go to C:\Windows\System32\drivers\etc and open the file called hosts in a text editor such as notepad or notepad++
Chances are if the source of this error for you is the same as me, you've done this before.
But you can't just straight up open the file, you have to copy it to another directory such as My Documents and open it from wherever you moved it to, make the changes you need to make and then copy it back to your \etc folder.
So if you open up the hosts file, you may have a line at the bottom somewhere referring to minecraft.session or something, basically if you have something in there with minecraft in, delete that line and before saving, ensure you have the version before you made any changes backed up. Save and exit out with that minecraft line removed, copy it back to the \etc folder and run minecraft. chances are you're problem will be fixed.
Sorry for the badly explained instructions. I'll try to put them in TL;DR form down here for those who know what they're doing
1. Navigate to C:\Windows\System32\drivers\etc and open the hosts file (has to be opened from another directory 2. Remove any lines that have minecraft in them. 3. Save and copy back into etc folder 4. Chances are your issue is fixed