Eye problem

Hello I just very recently took in a cat from someone whom wasn’t taking care of him. And 2 days ago he  was outside when he came back inside his eye was really squinted then we woke up this morning and his eye is squinted and swollen shut  and like his cheekbone area is very swollen and puss is coming out of it. I’ve been putting a warm towel on it. I’ve called all the vets in my area and they aren’t accepting new patients the ones who are can’t get me in for another 2 weeks. Any help would be VERY much GREATLY appreciated! Please and thank you.    Picture 1 is the day this started and picture 2 and on is today’s condition the red line mark is where the puss is coming out of is the next day which is today.

Sorry the pictures did not upload in order. The very last pic is pic 1 and the red are 2 and on

Hello - are you in the UK?  Are the vets to whom you've spoken aware of the symptoms?   The signs that you are describing are listed as an emergency because some of the causes of these symptoms could result in your cat being in pain or going blind.  In order to differentiate between them, I'm afraid that this eye would need to be seen.