Ms.nora, if your American fiance help you to apply for a Hong Kong visa as your sponsor, I guess that you can get a tourist visa with a longer stay duration. There is another option, Singaporean passport holders are exempt from a visa to Hk for up to 90 days, you can exit Hk to Shenzhen when the 90 days is up, then you return to Hk again as a new entry to get another 90 days stay. You don't need a visa to mainland China for up to 15 days, either, so you won't face the problems to apply for a visa to Shenzhen.