Yes, you do. Sorry, but you really do.
You've just been diagnosed with celiac disease or non-celiac gluten sensitivity, which means ingesting even a tiny bit of gluten can harm you. (See my article on How much gluten can make me sick? for more information.)
That being said ... have you ever looked at the inside of a used toaster? Toasters are absolute repositories for crumbs.
In order to make that used toaster safe, you'd have to remove the wire racks that hold the bread and scrub them completely clean (paying careful attention to joints and other crevices), and then you'd have to dismantle the rest of the toaster to get rid of all those left-over crumbs, especially those lodged in the spring mechanism that pops up the bread once it's toasted.
But you can't take the toaster apart they're not made to be consumer-serviced, which is why most people just live with the crumbs in their toasters. However, you can't live with those crumbs ... you'll most likely get really sick if you ingest just one.
So yes, you need a new toaster. Fortunately, they're not hugely expensive you can buy one online or at a big box store for less than $20 for a basic model. Splurge and get a nice one, and keep it only for gluten-free bread ... then you'll never have to worry about those gluten crumbs again.