Hello, welcome to SI, the best club no one wants to join. I'm so sorry you find yourself here but you are among members who have been through this horrible nightmare.
I have to be brief, but please find a good counselor for yourself to help you process your emotions. Also please get tested for STDS. It's been a month, and you are probably in shock and you've just boarded the emotional roller coaster from hell. One day you will be up, one day down, another just cruising along with sadness, depression, maybe clarity, and lots of confusion. All normal.
BTW, is the affair partner married? You should ask your husband for a written timeline on giving all the details of how/when/where/why the affair actually began. Are you absolutely certain he is no longer communicating with her? The first step to potential reconciliation (if you want it) is no more contact with affair partner, none, ever again, no phone calls, texts, emails, social media. All of it has to stop.
He's on the road, do you have access to the phone bills?
Please don't cheat, it will only make matters worse, why degrade yourself, and you would be no better than he is.
Do you have TRUSTED family or friends or member of the clergy if you are so inclined for support?
Does your husband want to save the marriage?
Check out the Healing Library, great articles just for some knowledge about infidelity.