How to fix my counter?

You can sand and repaint, then seal with an epoxy. The epoxy may extend the use time before the finish along the edges starts to wear off again. The edges take a lot of wear and tear; people rub up against the edges of the countertop when prepping food, putting left-overs into storage containers, washing dishes, leaning on the counter talking, if you have a breakfast bar it gets even more use, etc. Painting and sealing is a decorative solution, not a permanent solution. If you want to eliminate wear, you will have to opt for a countertop like Corian, granite, quartz, etc. Something hard-wearing and long-wearing. The beauty of Corian is that it hard-wearing, and can be sanded and smoothed and look as good as new if it is somehow damaged or stained. You can do research on line as to the best options for countertops to meet your needs.

Did you use an epoxy countertop paint kit or epoxy paint? Regular paint will not last, chip, crack, peel,

Jlnatty has it right that painting a countertop is only a temporary decorative solution, not a solution to permanently renovate it.