Expert Q & A Answers About IgG antibody test

If I give my boyfriend oral sex when I have cold sores, could he catch genital herpes?

I’ve always gotten cold sores on my lips and I have some now. When I give my boyfriend oral sex, can he get herpes from my cold sores? Is it bad to give him oral sex when I have cold sores, or are oral and genital herpes two different kinds of herpes?