whats the max weight? most people on this site would probably tell you to hold off on the belt unless you've got about 400+ pounds on the bar.
and i would agree with UAphenix, i dont think it is necessary to max out three times a week on squats. Im not sure if you a familiar with linear progression, but the system works very well and i think it would probably somewhat match up to your training program now. http://madcow.wackyhq.com/geocities/5x5_Program/Linear_5x5.htm
in regards to the original question, "So just asking if anyone else has experienced this."
No i've never felt anything like what you describe from maxing out squats with a belt. I did use a belt to train previously, but stopped because veterans and professionals told me to stop.
The only time i've ever had pain laughing/coughing/sneezing is from doing a shit ton of specialized ab work.