If I use personal hotspot on iPhone, will it use my Wi-Fi or data plan?

There are 2 computers in my house. One of them won't connect to the router. So I figure while my iPhone has Wi-Fi access, I can turn on personal hotspot and make the computer connect to the iPhones personal hotspot

I don't think that the hot spot feature on your phone will use Wi-Fi. It will use your 3g or 4g connection and use your data. I suggest you correct whatever it is the problem that keeps your computer from connecting to the router.

Personal hotspot is by definition, a cellular data connection. It shares your cellular Internet connection via Wi-Fi with other devices.