Thank you so much for your question. It is my privilege to be able to help you.
There is nothing wrong with treating the cyst with a cold compress, however, it is unlikely that it will work. Cold compresses are usually good to reduce inflammation after an acute injury. However, a cyst would more likely respond to heat. If it does not help, you should see your doctor to make sure it does not need to be drained or removed. If it seems to be growing or getting infected, see your doctor right away.
I hope this was helpful to you. Please remember to ACCEPT this answer if it answered your question so I can get compensated for my work. If you have any more questions please feel free to ask me. Take Care, Dr. SaulJE