When water doesn't come out of your shower head and you have pulled up on the diverter on the tub spout, you may have two plumbing problems.
First check to see if the inside of your shower head strainer is clogged with calcium and mineral deposits. If it is clogged, pulling up on the tub spout will not pull the water up to the shower head. Remove the shower head and soak it in a cup of vinegar for 24 hours to dissolve the build up.
If the shower head is not clogged, it may mean the tub spout diverter has failed. This is a minor plumbing repair and easy to replace. You may want to try replacing yourself prior to calling in the professional plumbing contractors. Most tub spouts are either screwed onto the pipe coming out of the wall or they have an o-ring that is compressed onto the pipe and an allen screw is holding the spout in place. Replacing the tub spout should solve the plumbing problem.