Is taking amoxicillin with oral herpes simplex outbreak safe?

Yes: It won't affect the herpes outbreak one way or another.

Check stress level: If you need to take antibiotics, and also have a case of cold sores, your immune system needs to be checked by your doctor to check in, and see why this is occurring. Make sure you have a balanced diet, stay away from 3 whites (sugar, flour, breads) to let your body heal. Increase whole foods. Take in nourishment physically, and mental relaxation is a must. Have your vitamin d3 level checked too.