If i had a cold sore in my lip and then touch and object, could transmit the cold sore to my genitals? i am so nervous about this

Usually not: If a person's first Herpes simplex infection was on his lips, and he developed (and continues to have) a good level of protective antibodies against that strain of herpes, then he should not be able to get a new infection elsewhere on his body from that same strain of herpes. However, life is not 100% predictable, so nature might seem to "break the rules" sometimes.