DON’T remove Norton at the moment!!!
Viruses often block the installation of security software such as antivirus programs. Unless your Norton is years out of date, it provides you with more protection than you will have if you take it off and can’t put a new one on. Deal with the virus problem FIRST and when your computer is clean, then you can get that Norton off and replace it.
Also, it’s not certain that Norton being out of date was the cause of the problem - there are many tricks that virus makers use to get past security software and it could be that something new managed to slip past Norton and make it less effective.