Has anyone ever had morton's neuroma for one year in their foot and got better without an operation?

Neuroma. As stated by dr kass - sure. The combination of injections therapy and orthotics give great results.
Sure. Injection therapy I find to be very helpful regardless of how long it has been there.
YES... I have found that most patients respond to conservative therapy, like pads, orthotics, injections, etc. I rarely perform neuroma removal surgery.
Yes. If you alter your shoe wear, so that they are not too tight or small and with good support that eliminate shock, this will help. Your podiatrist will also have solutions for this with stretching exercises, possible cortisone or alcohol injection, or orthotics to help with this condition on a conservative basis.
Yes. A morton's neuroma will not really go away. But proper offloading of the metatarsal heads with a neuroma or metatarsal pad can significantly help symptoms. A cortisone injection can help too.