This appears to be "Grand Prix" by Simon Ings, published in Omni's June 1993 issue. It is also apparently published in the anthology "Off Limits: Tales of Alien Sex" edited by Ellen Datlow.
From the text:
Formula Zero is a race for cars, not drivers. It is a vicious testing
bed for crackpot ideas, the way Formula One used to be till the
nineteen-seventies and the iron rule of Jean Marie Balestre.
Formula One’s rule book ceased to reflect technical progress around
that time. Formula Zero was conceived in the nineties as a way round
the role book and into the twenty-first century. Anyway, crashes are
good for business. My eyes are full of lignocaine. Underlids count off
the seconds. I tense my arse and spool the revcounter into the red,
just out of my line of focus. I pop the clench plate into my mouth and
bite down. The throttle glows green. I blink. The visor snaps down.
It’s made of Kevlar. A projector micropored to my head beams eight
external views onto the inner surface of the visor then setttles for
I’m in a different place. A green hillside. The track is a smooth
black nothing under my wheels, swirrling round the hill. I follow it
with cybernetic eyes. Gentry in the Ferrari is a blue proximity-danger
icon on my left near-side. He cuts me up on the first corner. I’ll use
him as a pacemaker. I’m so far ahead of the league table I’d be happy
to let him win. But if I don’t pass the post first, then Catharine’s
meme-bomb sits in me, waiting for the next victory. It only triggers
if I’m race champion. A kind of sick fascination is driving me. That
and a hope that the Progamme’s attack on the machismo-oriented Grand
Prix might dovetail with my own wish for vengeance on Maureen Havers.