HSV 1 is oral herpes. With herpes, the active lesions are more likely to be infective (for eg, visible cold sores around the mouth). But a person can transmit the virus even without having active lesions. As long as your partner is on antiviral medication, there won’t be risk of transmission to you.
Next Steps
It is not necessary to keep getting yourself tested unless you have symptoms. In case of genital herpes, using condoms can give some protection.
Health Tips
There is no cure but this is a treatable condition, and can be managed well medically. I would suggest counselling by an infectious disease specialist/ gynaecologist to help you get over your fear and anxiety.