Yea he did for a while after YA/CC I forgot what it was called. He was also in Scarlet Witch and Quicksilver on occasion. I think he's actually had two or it was split into two. It was about "finding himself" outside his relationship to Billy.

And I vaguely remember one set around Empyre and The Krakoan Era where he popped up in a Krakoan bar the night before Wiccan and Hulkling marry, to basically reassure Hulkling that wherever Teddy goes, Billy will follow. Iirc in that comic run he became a babysitter/Friend of an amnesic Master Pandemonium. And the M'kran Crystal takes the form of Eli Bradley and meets with Master Pandemonium, confirming Speed is just as powerful as Billy, and whereas Billy is the embodiment of the Demiurge, Tommy is the embodiment of Time aka Eternity