Is this a stye!??? Should I go to the ophthalmologist? ㅠㅠ

A few days ago, I had a sty that was so painful it felt like it was going to burst.. When I looked closely, a white pus-like substance was coming out.

So I squeezed it out with a cotton swab... and it seemed to settle down,

Today, pus has come out again... and my eyes are more swollenㅠㅠ

Should I go to the ophthalmologist because I have pus!??

Is it okay to just buy medicine from the pharmacy at this point?