Have you considered micro loading? Smaller than 5 lb plates or makeshift weights. Instead of going from 205 to that 210 you can't get you'll do 206 or 207.5 etc. This is probably the first compound lift people get stuck on.
Bought Adidas Olympics from Dynamic Eleiko in Washington. Chuck Taylors/Allstar would be better on deadlifts. Some friends go barefoot just for that if gym allows it.
When I started squatting I would be sore for a week and would wait that long to do it again. Over time technique improved, but the main thing that helped speed up recovery and make gains was eating more food. Lots of meat and milk. I don't know how much you weigh or how many calories you should...
It sounds like you don't have the right form in squatting. Without someone to instruct you in person some of Mark Rippetoes videos on you tube and his book Starting Strength may assist you.