Help please! cyst after clomid

This will be my fifth round of Clomid and I went in for an ultrasound prior to starting where they found a 36 mm cyst on the right side. My right side is the only side that works. I have a blocked tube on the left side. My doc told me to take birth control for a month and come back and try again next cycle. The cyst was 'producing hormones' my estrogen day 4 was at 223.
I am well aware of the fact that following your doctor's advice is important, but I am worried that the birth control won't do anything to shrink the cyst. Just prevent it from getting bigger. I want the cyst to go away, but I am hesitant to continue taking birth control pills for an entire month. Especially considering, if I skip this month and ovulate on the left side next month it's a wasted ovulation cycle. I am very frustrated and would like to know if anyone had success with getting rid of a cyst while taking birth control or if the cyst went away without it. If you did the birth control for a month, did it reset your system? As my doc says it should