Road trip across America?

So from October to June this year I’m going to SEA and Australia.

However a dream trip for me is to travel America. East coast to west coast. And then travel California and Pacific West Coast

I’m from the UK so can only stay in America for 3 months. Would this be enough time to do a road trip from East Coast (explore a bit of the east coast first like New England regions, New York and maybe Philadelphia. Go from east to west. And then explore California and then the pacific northwest and like yellow stone etc… etc…

Then secondly is transportation. Obviously can’t really hire a car/campervan (unless I can) but also buying one would be silly because I don’t live in the country so what would I do with it after? Honestly my best idea is to find a travel buddy who’s American when I got to SEA and ask if they would want to do a road trip around America with me.

Any advice for anyone who’s done this