The "international license" may actually hurt you more than it will help you in this situation. Several of my clients (from Europe) have legally traveled to the USA, and they have been involved in car accidents or received speeding tickets, etc. It has been my experience that, 9 out of 10 times, the average policeman will NOT recognize the "international license" and will give my client an additional citation for failing to drive with a valid state-issued license.
Now, I have been able to go to court and have this citation dismissed later -- but that is because I could prove my client had a valid driver's license from their home country, plus a valid international license, and they entered the US as a tourist, with a valid passport, etc.
While the cop may not be able to determine your illegal immigration status right after he pulls you over for a speeding ticket or a car accident...that fact may be discovered in court (or by the other driver's insurance company) soon thereafter. I'd recommend for you to seek an immigration attorney near you; they can advise you on the best legal way for you to be in the USA.
You may drive with a licence from your home country for a period of 90days if you are visiting as a tourist.
Most local policemen do not know about international licences and do not rightly care either, you need a valid licence to drive in America.
With the present immigration climate, your immigration status can be discovered if you are stopped by a police officer and you are not able to provide valid immigration documents.
Be advised that the greatest challenge you face is not the international licence but your illegal immigration status.
That is what will lead to deportation proceedings.
Therefore as a matter of prudence, it is advisable to contact an immigration lawyer to rectify your immigration status first and foremost.
You do not need to draw more attention to yourself by driving, use public transportation.