Yes coughing of thick mucus or any mucus during a cold is usually a good sign that your cold is about to be gone.
Your mucus contains bacteria that the body is trying to get rid of in order to fight off the cold so always spit the mucus out when you have it in your throat.
Swallowing the mucus can make your cold take longer to go away and can make the cold worse.
If you have some blood in the mucus that you're coughing up it could just be part of the infection or it could be something more serious that you should see a doctor about.
If you see a lot of blood in the mucus or are coughing up a lot of blood then you need to get to the emergency room.
But just normal mucus is usually okay.