does your gym have a power rack? You can do back squats on that if you learn how to bail out if there's a problem, or just use bumper plates. My old gym only had a smith machine too, that was the reason why I went and found a new one.
Chances are if your program is designed by a professional, it's calling for back squats or whatever squats for a specific purpose, usually because those specific stresses and muscles worked are essential to the rest of the program and feed into the rest of the lifts. If you switch things up you're no longer doing that program, and you risk overexerting a muscle group while neglecting another entirely.
I made the mistake when I first started of trying to substitute zercher squats for back squats, which absolutely killed my deadlift progress by overstressing my lower back, and didn't make much progress on my hamstrings/glutes because they don't engage as much compared to back squats. Then I changed gyms and started following my program to the letter, and my squat more than doubled in like 2 months, lol. Just something to think about I guess.
edit: also it's not ideal but have considered learning to clean the weight up to your chest and then going into a set of front squats? You'll probably run into a wall here eventually since you can most likely squat a lot more than you can clean, but it's doable I guess. Then again, it's another substitution, so yeah.
is the pain mainly on the bottom of your foot, almost like you're standing on something sharp and it feels like the skin/muscles on the bottom of your feet are really tight? Maybe radiating into the ankle or a tightness/pulling in your calves too? It sounds a little bit like Plantar Fasciitis, which can be really fucking painful, but can be (hopefully) solved with orthotics/shoes to correct whatever's wrong with your gait.
http://en.wikipedia.org/wiki/Plantar_fasciitis
could this be what you have?