I have hsv2 and have a small breakout in my
Definite chances of spread...
Assuming the outbreak is indeed due to HSV2, there is a definite chance of transmitting ti to your partner. Though rate of transmission from female to male is low (some reports predict less than 10%), exact chances are unpredictable.
So I'd suggest you to get this checked. If it is indeed an HSV outbreak, I'd recommend your partner to start antiviral medications which will lower transmission rates significantly.
Hope this helps. Let me know if you need clarifications.