I have a blocked tear duct. Cyst on my eye I have eye drops. Was told by gp to bathe in hot water, now worse. What can I do to get rid quicker?

Eye exam. Warm compresses for 10 minutes 4 times a day will help the cyst if it is a sty or chalazion . If the tear duct is blocked this will not help, it needs to be examined by an ophthalmologist.
More info needed. A blocked tearduct does not cause a cyst on the eye. If you mean a cyst of an eyelid gland, a chalazion, warm compresses, "lid scrubs" with baby shampoo, omega 3 fatty acids by mouth, and antibiotic/steroid drops may help. If all else fails, surgery (excision and or drainage of the gland) is the way to go.