I will never overdo ear pick.pick my ear too much

They way you are using ear pick, it is a verb here. So the verb form is "to pick ear".

Last year, justaround this time of year, I got into ear pickstarted picking my ear because it was comfortable.¶

Based on the fact that "to pick ear" is a verb, I made these changes

However, it caused otitis externa, and I couldn't put onwear an earphone because of pain.

1. You wear an earphone not put on
2. It's clear because of otitis externa you couldn't put on an earphone

She said ear picking ear with hard materials can hurt the ear, so wipcleaning offit softly with a cotton swab is enough to clean the ear.

1. Again converting usage of to pick ear to sound like an action
2. Stylistically - keeping it shorter and simpler also conveys the meaning

I dumpedstopped using my ear pick and I'since then I have used a cotton swab once since then.

Here you are using ear pick as a noun and hence it's correct. But dumped is used in the sense that you dropped something at once. Better to imply that you stopped using it completely.