Hello there. My name isXXXXX and I am very sorry to hear about Caeser. It definitely sounds quite possible that he has some allergies and they are effecting his eyes. The first thing you can do is give him benadryl at a dose of 1 mg per pound every 8 hours. this will reduce inflammation and the effects of his allergies. But also you can use artificial tear drops otc to help flush out his eyes and remove any dirt, dust, debris that could be causing irritation and finally you can get drops called polysporin eye drops OTC that you can use twice a day that will help remove any bacterial component that could be causing this irritation and inflammation. You should see improvement in just a few days. the cool compresses are a good idea to help remove any excess drainage or debris. Again use artificial tears to flush his eyes then use polysporin eye drops twice daily to help remove any infection. If anything gets worse though of course have him seen by your vet. If you have any further questions or concerns please do not hesitate to ask. Also please do not forget to rate my response so I receive credit for my time. Thank you!