The -RT triggering system is much newer than the 550EX, and I think the only way you could trip one is if you added a YN-E3-RX radio receiver to the foot of the 550EX. But some B&H and Amazon reviews say that this combination does not work, and the 550EX is not on the list of flashes that are compatible with the trigger.

You cannot use the built-in "smart" optical slave in the 550EX, because the YN-600-TX is only a radio master, it is not an optical master. And the 550EX has no "dumb" optical slave to be set off by any flash burst.

You could use a YN-600EX-RT II as a "smart" optical master to the 550EX, but again, how much control you'll have will be more limited than you might expect, as the 550EX is only capable of groups A and B, and can only be controlled by TTL ratios over the "smart" optical system, not manual power ratios (1, 1/4, 1/16, etc.)

If you still want to use the smart optical system, it might be cheaper to get an ST-E2 (which is the same era gear as the 550EX) or the Yongnuo clone of it. On the used market, these should be very cheap, since most folks prefer radio triggering for remote flashes.

You could also treat the 550EX like a manual-only flash put it in M, dial in the power setting, and use manual triggers, like the Yongnuo RF-603II or Phottix Ares.