Background: I've never been on Tysabri, and have been on Ocrevus for almost a year. Caveat: I am an MS patient, not a doctor.
Both drugs suppress the immune system hoping to prevent MS attacks. Our immoral for-profit health insurance corporations tend to want to start MS patients off on inexpensive drugs and then progess to more expensive drugs as a patient's symptoms get worse. But remember, you're in charge of your health and should be the ultimate decision-maker.
Many of the MS drugs have various side effects that you'll want to read up on and talk with a trusted doctor. People often are started on Copaxone which is given by the patient giving themselves shots. While giving yourself needles in the legs, arms and belly may sound odd, it's not that bad; the side effects can be worse than giving yourself the shot. But it sounds like your neurologist is ruling out that drug.
Tysabri has a low-odds "side effect" of the patient getting an incurable, fatal brain infection. (Obviously suppressing the immune system can open one's self up to problems.) I believe there are tests that can be done to detect that, but I opted not to use that drug, mainly for that reason.
Ocrevus is a recently FDA approved drug that quite a few patients are migrating to, it seems. It's an immuno suppresant that is derived from an older lukemia drug. Since the manufacturer got a new patent on the changes of the old lukemia drug, our for-profit drug system means Ocrevus is wildly expensive. But it is considered today the "gold standard" (no pun intended:) of MS drugs, and statistics rank it as the best or one of the best in doing its job.
As you know, Ocrevus is given via an IV every six months, which to me is nice after giving myself Copaxone shots every other day or drugs in which you have to take frequent pills.
and she said it seems severe to start me on an IV.
I can see her point, but all of these drugs are "severe" -- just like MS. :)
I would view her point in the idea that you're jumping to the "top" of immuno-suppressing drugs. If Ocrevus does not work for you (that's a possibility) you're sort of moving down the ladder of immuno-suppressants to try something that does work. To me, that's not a big issue -- finding something that works is the goal here! -- but others may weigh that equation/algorithm differently.