Welcome to ThisIsMS! I also have no experience with the Avonex or in my case any of the injectibles. My neurologist tried to sell me on the injectibles but I did my own research and decided not to use them. Amongst other things, I read somewhere that something like 60% of people with MS do not use them.
I was diagnosed three years ago and have done well with high dose vitamin D3 (5,000 IUs a day) after first getting my vitamin D level tested (a simple blood test) and started on 10,000 IUs a day to get my vitamin D level, which was extremely low, up toward the high end of the normal range. There's lots of very hopeful information about vitamin D for MS on this site and on the web. Vitamin D is not just a vitamin, it regulates gene expression and modulates our immune system. There have been some very promising studies of Vitamin D's affect on MS, though more research is needed. And there are indications that most people with MS are vitamin D deficient.
I'm guessing that what your doctor may have been hinting at is that as we age, many or most people with "Relapsing Remitting MS" eventually convert to "Secondary Progressive MS". The injectibles don't work for Secondary Progressive MS, so once you are diagnosed as secondary progressive (if you ever are), you quit taking the injectibles.
In addition to taking Vitamin D3, I also am on a low saturated fat diet. You might want to read up about the Swank Diet, and there are several other MS diets out there too.
Good luck and I totally support everyone's right to do their own research and make their own choices about what strategies to use in fighting this disease. I am not a medical professional. My comments are just my opinions and experiences, not medical advice.
By the way, I am a little younger than you, but I have grey hair, and especially now that I have MS, I definitely feel like a senior citizen.