I have herpes, but I don't have a rash. Am I still infectious?

Sometimes. Women with genital herpes can sometimes be shedding virus without having symptoms. One can talk about medications for prevention at a visit with a primary care doctor. If one's spouse or partner already has herpes and antibodies (blood tests can be checked), then it may be less likely to pass herpes to the spouse or partner.
Depends on Sex. Not whether you are sexually active, but what sex are you. A female (and rarely male in urethra) can have active lesions which cannot be seen. It is always wise to use protection. If you are unmarried, it is better to abstain. Dr. J.