HSV1 can't turn in to HSV2, but HSV1 can cause blisters at the lips (cold sores) and in the genital area.
Still, lips and face are preferred sites for HSV1.
Same is true for HSV2.
HSV2, usually, causes genital herpes, but the virus can be transmitted to the face, too.

go to the store and pick up some abreva and this will shorten the time you have the cold sore.