If you don't mind paying a small fee, then checking to see if your license is suspended is easy enough at dmv.org/driving-records.php.
The fee (if applicable), and the process involved, depends upon which state your license is held.
The DMV discourages the use of website which claim to offer free driving license checks, but does not say why. Perhaps the DMV is concerned such sites do not have access to the correct information, or that these sites are actually data scams.
If you did want to use such a site, this again depends upon where you live. For example, if you lived in Washington State, you could try: fortress.wa.gov/dol/dolprod/dsdDriverStatusDisplay
Bear in mind this site this will only give you a yes or no answer as to whether your license is valid or not. Drivers in Georgia can check online.dds.ga.gov/DLStatus. Most states would have similar yes/no websites too.
Other sites provide a more general service, often used by employers to check their employees have a good safety record. These include 4safedrivers.com and drivingrecord.idrivesafely.com.
For another Blurtit response to this question, go to How Can I Find Out If My License Is Suspended For Free? or check out this YouTube film as to whether American drivers need a license at all: