Hi Ravl,
No judgement on the weight. Your on the LP planning to get stronger - that's a great start.
Feeling really spent after near limit squats is normal. Feeling faint, as in being close to passing out - that's another story. As you noted, the latter is associated with cleans and presses racked incorrectly, but not usually with squats.
Were you breathing at the top? That's where you're allowed to take a few breaths before bracing for another rep. The valsalva only lasts a few seconds at a time (even if you're grinding out a final rep) and the top is where you get to take new air. Is that what you were doing?
I don't think you can over-squeeze your abs, nor do I think that a belt would assist with this problem (which I wager right now is breath related, but no way to know for sure). A belt is a great tool to acquire though.