So, I know that eye infection is not comfortable, and you need to take care of it positively. Anyway, apart from effective treatment, you could resort to warm compressor, because cold compressor is used to deal with physical injuries. By applying warm compressor, you could relieve some bad feelings and quicken the speed of healing.
Well, in my opinion, you should use cold compress, which will be effective for your situation. As we know that eye infection is caused by bacteria, viruses or environmental agents, such as pollens and other irritants. And when it happens, it can make your eyes feel itchy, red, burred. So when you apply cold compress on it, it will just relieve the symptom. Also, you can put some tea bags on your eyes. As we know that tea bags contain a high concentration of the chemical epigallocatechin gallate, which acts as an anti-inflammatory agent that can relieve your symptom. Anyway, you can have a try.
The warm compress will do better than the cold compress for the eyes infection. As we know, the cold compress will be suitable for the ankles hurt, strong knock around the eyes and so on. Using the warm compress, you could find that the eye nerves will be worked in the quick way. The bacterium will be out after the warm compress. It is good for the eyes infection. However, you should keep on using the medical care.