No. That's breaking the rules of a Nuzlocke. You can only catch one per route.
If you went to Rusturf Tunnel first and found Whismur, then find a Whismur in Route 116, you can implement a "dupes clause", which means that if you have already caught that Pokemon before, you can catch a new one, usually up to 3 tries. That's basically the only way you could get out of the dilemma, but its too late.