So yesterday and this morning my Jeep has been turning over very slowly. Like instead of the normal "Click click click start" it was more like "Buuuuur... Buuuuur....... Buuuuuuuur..... start". I drove to my school which is pretty far and when I pulled into the parking lot my dash and radio both flickered off and then on again. Now I'm sitting in class a little worried if my Jeep will even start. Do you guys think it could just be a bad battery? Because it seems like the battery is still dead after I drove all that ways I'm worried it could be the alternator.

You have a couple of options here, you can have it jump started and if it starts you will be able to get home. The battery and alternator can both be tested for free at most autopart stores.

Are the terminals clean? Test the battery and alternator.

Jump start or push start (if you have a manual) the Jeep. Then with the engine running, disconnect the battery. If the engine shuts off, probably means the alternator is bad and not supplying enough juice for a spark. At least that is what I was told to do years back with my old VW Beatle.

Whatever you do, do not disconnect the battery when the vehicle is running. You may end up damaging circuits in radio, computer modules, basically anything with a circuit board.

check grounds too

What is the voltage at the battery terminals when running?

PLEASE DO NOT DO THIS!!!! Worst case scenarios include: battery blows up... You get acid in your eyes/skin, fry your PCM, blow other electronics, fire...

Test your battery and alternator with a multimeter. I like to test the battery after vehicle has sat overnight, test battery with vehicle off. Then start vehicle and test battery again, then put MM on alternator leads to see if it's giving you good voltage.

Start first by removing the terminals and scrubbing them sparkling clean and retightened. If you have a multitester/voltmeter, check battery voltage with engine off and then with engine idling. There should be about a 1.5v (+/-0.3) difference in the 2 readings. (around 12v versus 13.2-13.8v with alternator)

Or you can drive it to an auto parts store to have it load tested. If the battery is over 3 yrs old, it's highly likely you have a bad battery that's not holding charge from the alternator, which I see as more common on TJ's versus a failing alternator.