I've taken gabapentin for over 10 years for CIDP - nerve pain, and I take a LOT of it.
It's never helped with anxiety that I've ever noticed and now barely helps the nerve pain.
It is a good drug however, with no noticeable side effects or drug interactions.
Actually, gabapentin is used for anxiety, in higher doses than those used for nerve pain. It's off-label, of course, but isn't everything these days? I only know this because my psychiatrist is considering it for my anxiety, and that forced me to research it, otherwise I'd be clueless. How well it works is another matter. But heart rate isn't causing your anxiety here. Some people get an increased heart rate from anxiety, but most just feel like they do and actually don't. Also, slowing down your heart can be dangerous if it's already a bit on the slow side, as it is with athletes. Despite my horrible anxiety, my heart rate is relatively slow because I meditate and exercise a lot. If you really want to work on the symptoms of anxiety attacks, a therapist who specializes in anxiety treatment will be able to teach you breathing exercises and relaxation exercises to help with this. Medication works differently, working to reduce anxiety by altering brain processes, not by slowing down the heart unless you have a heart problem that would independently require that.
Although both these medications help with nerve pain and associated ailments neither is an antianxiety agent. Cyclobezaprine is a muscle relaxant and similar in structure to the early tricyclic antidepressants and may therefore help provide anxiety relief.
Talk to your doctor about more specific anxiety relief if you feel it's needed.