Remove the lid to your toilet tank. Examine the handle to see if it appears to be loose. If so, then locate the toilet handle nut on the inside of the tank. Toilet handle threads are the reverse of common threads. Apply your channel lock pliers and turn counterclockwise to tighten. The threads are reversed so that as you continuously push down on the handle, the nut won't come loose. Don't overtighten or the plastic handle may break.
If the handle is tight, inspect the mechanism and see if the chain or linkage is tangled. This is a common problem with metal chains because they rust up after a while. Insert your scratch awl and untangle the linkage or chain. Spray lubricating spray on it if necessary. Check the small clip that connects the chain end to the handle–it often jams up too.
Follow the same steps above to untangle it if needed. Twist free with your pliers if it is really jammed. If the chain or linkage can't be freed, then purchase a new flapper, which will come with a new chain and linkage clip.
If the problem still exists, inspect the back of your handle where the nut holds it in place for lime buildup. This is common with metal handles. Lime can jam up the area between the handle and nut, preventing it from pivoting freely. Brush on some vinegar to the area with lime, using your small paint brush. Let it set for about 10 minutes. Loosen up the nut by turning it clockwise (reverse thread) and then remove the nut. Unhook the flapper chain from the handle. Remove the handle through the front of the toilet. Clean all parts with vinegar and water. Reinstall in reverse order.