Check your local gun shop for 38-55 ammo, it's still in production.
Remington and Winchester ammo is held to black powder pressure levels. But burns smokeless. If your rifle is in good condition it will work fine.
Watch out for old ammo, Many many years ago, they did make a high pressure load that may not be safe in your rifle. Current stuff is fine.
(Your chances of finding that high pressure stuff is about akin to a major lottery win)
Your original post indicates that you now have a 30-30 barrel, if that is the case, you're still fine with current ammo. The action can take it, the weak spot in the older rifles was the barrel. Prior to about 1910 or so, Winchester did not use 'smokeless' or 'nickel' steel barrels.
I said "or so" because they used up old inventory gradually, and there is no firm switch over date.