Welcome to the club bro. Life just gets more fun an exciting now. I wish I could tell you its all sunny beaches and pina coladas from here, but no. Die pretty much covered it. It could be a month or two before things settle down some. Don't do anything stupid that can make it worse until the initial pain settles down, or you can make it worse to the point where you bruise your spinal cord and end up with sciatica so painful you scream your head off and go straight to the ER. If you insult your spinal cord enough, you can wind up with permanent nerve damage in your legs and muscle atrophy. This is nothing to play with. Get to a specialist, get your MRI. Look into injections if needed. They have the potential to help tremendously with pain.
Things to know... once the disc has bulged or slipped. Even if you feel 100%, it can happen again much easier. Start looking into alternatives for squats. If you keep re-injuring the disc/vertebrae it can also lead to facet arthritis and spinal stenosis. At that point, shots will help but the second you irritate the arthritis, the injection usually stops working.
My spine is fairly jacked with collapsing discs and everything i said above. I've never herniated a disc, but my understanding is it can be all this and some. There are a lot vets on this board that have multiple fused vertebrae. They can chime in. I wish I knew all this back when I used to watch Blood and Guts several times a week with aspirations of competing around 300lbs. You don't have to train that nuts to get that big. Train smarter not harder..
Best of luck..