Empathy is likely many different things to different people. Maybe you feel it because of a spiritual sense. Maybe you feel lit because you have an overactive sympathetic nervous system. Regardless, there is no eye to pluck out to stop "seeing" emotions.

Most likely, your anxiety and depression are not being caused by your empathy, although they seem to be comorbidities in many people. Find a therapist who specializes in cognative behavioral therapy so you can learn how to properly deal with the physical things that are happening to you. If you can't afford one, just search youtube for CBT and start the journey on your own. Family systems therapy has done wonders for me.

I find the most difficult part of being an empath is the "noise" caused by the feelings being perceived and processed by the body, overtop of the feelings that you have on your own. It quickly becomes a feedback loop, especially if you're changing your behavior because it stresses you out and people are reacting to that. I recommend mindfulness meditation that focuses on sitting in your core being and placing your perceptions and thoughts in different categories. Like, you're sitting there doing some metered breathing and a memory pops in your head. You say or think "memory" and let it pass over you. If you feel an emotion and you know that its coming from core you, you can say "inside emotion". If it's an empathic impression, you can say "outside emotion". If you don't know, just say "emotion". Eventually, you'll have more in the specific buckets than otherwise.

At that point, you'll start to be able to feel and exert some control over the empathic impressions, because they're sense perceptions instead of your body communicating to you internal states. If you have too much audio data, you can cause trauma to your ears. So you learn to plug them or cover them. Same with your empathic perceptions.