I have bad pain in my lower left side. Occasional nausea and bad headaches. Pain in side worsens when I cough. Been told have a 3cm cyst on left ovary?

Ovarian pain. Pain from the ovary or left abdominal pain is always a concern. A MD usually acts on the information, but a small 3 cm ovarian cyst is the unlikely cause because it is only one inch+ in size. Call your MD and explain your continuing symptoms.
Need to see a Dr. If you are known to have a cyst on your ovary and your pain has suddenly worsened, this could mean that the cyst has twisted. This is called ovarian torsion and can be a medical emergency. There could also be an abscess developing in the ovaries or fallopian tubes as well. You need to either go to ER or see your family physician to get blood tests and an ultrasound scan done.