Yikes! Sorry that happened, you must be in a lot of pain! Keep up with the aloe, and take advil every 4 hours to help with the pain until you see your doctor! Try using aloe without any other "stuff" like lidocane in it, it might be the lidocane that is making it sting. If the burns are that bad, you should call your doc ASAP! If you are in too much pain to sleep, call your doctors office, they should have someone on call.
You need to re-apply more often than every two hours. An SPF of 45 only protects you from sun damage/burn for 45 minutes, SPF 15 for 15 minutes....you get the idea. Maybe this is common knowledge for most of you, but I didn't know until recently, I just knew a higher SPF was better, but didn't know it had a relation to minutes of sun protection. So you have to re- apply 45.....every 45 minutes. Who knew? (I didn't until recently, I thought like you did that every 2 hours was often enough.)
I hope you get some relief soon!