Gym membership where I live is cheap. Like it would take years of monthly gym payments to equal the cost of a good set of weights and stuff to work out with. Husband has a lot of free weights so I do lift at home but do yoga at a studio, and when I did use the gym, I took aerobic dance classes, did stairmaster and watched people lift weights, used machines and lifted weights myself and didn’t have to take up half the bedroom with weights.
I personally enjoy going someplace to work out a lot more than doing it at home, but I do both.
Clothes don’t matter, don’t you have any loose shorts? That’s what I see guys wearing at the gym, they are probably like $5 at Walmart.
ETA: on your actual question yes home workout can be effective, of course. Plenty of people do fine just going out for a run and doing some pushups, pullups, unweighted squats, planks, etc; and yes I enjoy more going to the gym, and once there, will work out - at home always something else needs to be done and it’s harder to focus.
Kidneys are right there. Get checked out please.