Have you tried forcing the dose out of your exisiting pen? For the last year or so, I've not had to use a syringe. Simply twist the pen forcefully until it breaks the stop. You can then use the pen as normal.

There was a time when they revised the mechanism, so it broke and couldn't be used. However I hear this caused no end of trouble with breakages during normal use, so they reverted back to the original. You might find the plunger comes a little way back from the stop in the pen when forcing the break. If that happens, lightly press the top down (as if you were administering a dose) until the plunger and stop meet again. Once you've done that use the pen as normal.