A cold sore just sprouted on my lip and I'm monogamous, does that mean my girlfriend of 4 years gave it to me by cheating?

No. The virus that causes cold sores is acquired by contact, but once you have it it's yours for life. Most people pick it up as children from older relatives.
No. The first time you get HSV1 can vary from a single sore on your tongue to multiple invading your whole mouth/throat. It is often acquired in childhood and may never return, or show up as a focused sore near you lip intermittently over a period of years.