I would not try much droving, like Brian said. If the alternator is not charging you will not make it far, and probably shorten the life of the battery if there is a problem.

Time to start troubleshooting.
With the engine running what is the system voltage. A couple different methods.
I guess there is a way for the gauge cluster to show it on the mid. I haven't done it.
Or just grab a volt meter and check the voltage, somewhere like directly at the battery or at the jump start connections under the hood.
Also, the tech I work with routed the drive belt wrong. At a glance it looked correct, it spun the fan and everything. But wasn't tight enough to spin the alternator or was spinning it backwards or something. All I know is I put the belt on correctly for him and it worked great.

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