This sounds like a low or dead battery issue. If your battery has gotten low or close to dead it's going to take awhile for your alternator to charge it up. If you just jump start it (in a dead or really low condition) you're asking your alternator to do double duty - charge and supply full voltage to all your ignition, lights etc... that explains why rough running conditions. Alternators are like a very slow battery charger - they don't blast VOLTS back into a battery instantly while providing all your electrical needs.
I'd suggest charging your battery on a REAL battery charger for at least 6 hours. If after doing this you come up dead again then it's either a tired battery or an alternator. You could have the battery load tested also but it has to be fully charged to have this test done.
If the rough running continues - put a voltmeter on the alternator & make sure it's putting out 13.1 - 15.5 volts while running - if not then you have an alternator issue.