It sounds like you might have a fungal infection, or an athlete's foot (known as tinea pedis). This can be picked up from someone else, or from a surface--gym or dorm showers and bathrooms are notorious hot spots for fungi and bacteria. It's not just for sports players or people with poor hygiene-up to 15% of the population is thought to have tinea pedis.
There are plenty of over the counter medications that will numb your foot up to stop the itching, and others that will kill the fungus. Some do both. Lotrimin and lamisil are commonly used.
This can also cause the cracking or cuts between the toes. (here's actually a picture of a pretty bad case http://en.wikipedia.org/wiki/Image:Athletes.jpg )
Be careful, because this can be spread to other parts of your body, such as your groin, armpits, navel, etc. Always wash your hands if you must scratch your feet.
If the meds don't work, then you should see your doctor, as there may be the need for oral medications, or you may have a different skin condition.
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I would not put alcohol on that. Not only will it dry the skin out further, but it can actually damage the skin and make it irritated (as I'm sure you feel when you use it).
Most creams can be applied directly to the cut, because they are medicated-just be sure to check the label of the brand you decide on to see if it warns against applying to open skin. However, if it irritates the cut, you can apply regular bacitracin or neosporin to the cut before the cream is applied to the foot.
It's important to finish out the treatment, because athletes foot can come back easily.
Hope this helps,
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