I think I have a stye but it's in the far corner of my eye. There's no bump on my eyelid but I have all the same symptoms as a stye?

Could be. Early styes that are internal, will cause diffuse swelling and tenderness. Only later, if untreated, will it localize to make the bump that you are expecting. I hope you are using very warm, not hot, soaks 5 times per day to help get rid of this.