My partner has cold sores, does it mean he cheated?

Probably not: Cold sores, assuming that is what these are, are usually located in the mouth. If these are genital lesions they are probably herpes. If that is what they are it still does not mean that he has "cheated". He may have gotten these long before he met you and they are now recurrent. If you have suspicions there is a communication problem that you may wish to explore further.