Were these charges at one time or separately?
If they were separate charges, then the immigrations officer will certainly refuse entry because you are a repeat offender.
You should find out if you can leave the country as you have been arrested and there may be some special conditions you have to adhere to. You don't want to make it look like you're trying to jump ship with your arrest.
Immigrations at the POE will certainly know about any arrests and will definitely give you a hard time about it, but it's at their discretion whether to allow you to enter the U.S. or not.
I have a friend who had a DUI (it was his only arrest and he is a good person) who tried to reapply his
TN visa. His application was denied after a long scolding about his DUI, but was still allowed to enter (his current visa at the time hasn't yet expired). He was warned that any future arrests will prevent him from entering the country.
He later hired an immigrations lawyer to get a new TN with no issues.
Getting off-track: In these hard economic times, when I reapplied for my own visa recently I included a resume of my extensive charity work and involvement in various organization, and my volunteer work to show how I made a huge contribution to their community (more than the typical American citizen) and not being a burden to the country. This luckily worked in my favor this past year, as the immigrations officer was questioning my application and giving me a hard time about returning and living off their country. Unfortunately he didn't read all of the documentation I provided, so I told him to refer to my resume which he was holding which I then recited word for word to make my point. He reluctantly accepted my application.
So you should definitely exploit any good deeds you have done, it would only help your situation.
Since you are not reapplying for a visa, you probably won't have an issue, but be sure to be honest when answering any of their questions.