Can my lip cold sore spread to the genital and eye areas? what should i do to prevent the cold sore from spreading to other areas? i want it contained

Low risk, no worry: During the very first infection, HSV can infect other sites, especially eyes or fingertip. But this almost never happens with recurrent outbreaks. If you've had cold sores a few times, there is no risk. To be extra safe, it's a good idea to wash or use alcohol gel (e.g. Purel) frequently and try to avoid rubbing your eyes. But little risk if you forget. No risk at all for genital infection.