Could BPH be making my right testicle much larger than my left one?

No. BPH is a benign enlargement of the prostate gland. The testicle sewlling is usually from other causes such as hydrocele, trauma, or cancer. If there is a discrepency in the size of your testicloe, see your physician for further testing.
No, not related. Must be other causes. Please have your urologist check it out. Will probably advise a scrotal ultrasound. Good luck.