Well, I just highly doubt that the loss in your bad ear is due to the tumor in your good ear. Just doesn't sound right to me. I had loss in my non-AN ear, they think due to a virus, when I was 37. It wasn't bad at first, but through the next decade kept worsening until it was highly suggested a HA would help...which it did. Then 2 years after I got my HA I found out I had an AN in my perfect hearing ear (arrghhh).
I strongly strongly advise you not to have surgery for a 3 mm AN. I remember my neurotologist told me if anyone wanted to perform surgery on my perfect hearing ear to remove the tumor to get up and run. Mine was 1.7 cm....so quite a bit larger than yours. I think you should go see another doctor or two. I'd also find a neurotologist, not just an ENT. There's always a gamble to watch and waiting. If it were me I'd go and have my hearing checked out every 3-6 months to make sure it is staying the same (and of course an MRI as recommended by the doctor). the moment there was any change in my hearing, I'd start researching my options.
Radiation would probably stop the growth, but there are still side effects with that. One of them was I got tinnitus in my perfect afterwards. But please...you have all the time in the world right now to investigate.