suddenly a tyre blew up/out
Are they both possible?
I think "a blowout" in AmE is "a puncture" in BrE. I don't know if that means they say "my tyre (sorry, tire) blew out".
As Bhai said, "to blow up" means to inflate or to explode. I suppose it is technically possible for a tyre to blow up (explode) but that would be a very unusual occurrence. Perhaps if you inflated it and inflated it and inflated it beyond its capacity it would finally explode. In that case you would "blow up the tyre until it blows up" (inflate until it explodes)!