As much as I hate it, the unfortunate truth is that the gym can be an intimidating place, especially if you're particularly shy, embarrassed or introverted. My main suggestion would be to either 1, hire a decent personal trainer (judging "decent" can be an issue however), or 2, find someone to train with, preferably someone who knows what they're doing, but sometimes there's confidence to be gained by just going to the gym with a friend, even if they're as clueless as you.
If neither of those are an option, then I would suggest picking one exercise from each of the following sections, and try that (they're mostly the most basic variations, and I've put them in order of preference, top to bottom).
You should be able to find decent tutorials online for the majority of them. Try and not sweat technique too much to start with, you can read all the information in the world, watch all the tutorial videos and discuss with everybody online, but it won't make sense until you get some time under the bar.
Because of your size (and this is a guess as I haven't actually seen you), you may find the dumbbell variations of the exercises easier; they should allow for a greater range of motion (if you've got a big chest, then a barbell will hit your chest and stop the movement more than dumbbells).
- Standing overhead press (barbell or dumbbell)
- Seated overhead press (dumbbell)
- Incline press (barbell or dumbbell)
- Bench press (barbell or dumbbell)
I much prefer overhead pressing to flat (bench) pressing for various reasons, shoulder health and more core activation being the main reasons, but try and see which variation you prefer. Overhead work can take up more room, and most gyms have benches near the dumbbell rack, and most people do dumbbell bench work, so if that seems like a safer option for you (copying what most other people are doing), then go for it.
- Row (barbell or dumbbell)
- Row machine (weight, not cardio)
- Cable row (machine or cable station)
- Pulldown machine
Barbell or dumbbell bent over rows are good, but I can see how they could be a bit embarrassing because of the bent over position you put yourself in. A lat pulldown machine / row machine is a pretty good alternative if it's something you're more comfortable using. I know they're not freeweights, but they're one of the few situations where a machine will do the job.
- Sumo barbell deadlift
- Sumo kettlebell deadlift
- Deadlift or Rack pulls
- Romanian deadlift
- Single leg deadlift
- Kettlebell swing
These aren't actually in order of preference, they're more in order of what I think you'll find easiest. Sumo deadlifts look a little funny if no one else in your gym performs them, and rack pulls (deadlifts where the bar is up on blocks, meaning the starting position is higher than the floor) can be noisy depending on where you do them. Single leg deadlifts require a fair amount of balance, which can be a bit embarrassing if you can't get it right, and kettlebell swings are one of those exercises where a lot of people teach it wrong.
If you don't want to try sumo deadlifts with a barbell, then I'd recommend you do sumo deadlifts with either one or two kettlebells. Once you get proficient at them, you can look at kettlebell swings (great for fat loss), or moving onto barbell sumo deadlifts. Also, if strength is an issue, you can use less weight with kettlebells.
- Supported bodyweight squat
- Goblet squat (kettlebell or dumbbell)
I know you said you can't squat, but hear me out. A bodyweight supported squat, is a squat where you hold onto something with your arms, and pull yourself up as you stand up from the bottom of the squat position (something like this, though if your gym doesn't have any suspension trainer gear, you can do the same thing on a cable machine, or even just holding onto something sturdy and leading back a bit as you squat down).
Once you can, I'd recommend moving onto goblet squats. They're an excellent beginner squat movement (not just beginner to be honest, I've seen champion powerlifters use them in training).
- Farmers walk
- Arm work
This can actually include pretty much anything else you'd like to try out. I'd recommend planks (if need be, you can do them with your hands on a bench as a more upright angle will make the exercise easier) and farmers walks (basically grabbing a couple of heavy dumbbells and walking around the gym carrying them, though it's an unusual one, so I understand if you'd rather not) as they're both excellent exercises that I think everyone should do. Arm work because some people like it (I don't by the way, I never bother with direct arm work).
Hopefully you'll find something useful here, one thing I would say is that even if you feel shy or embarrassed in the gym, you're there trying to better yourself and a lot of people will respect the effort you're putting in. It's a lot easier to sit on the sofa, eating pizza and watching Netflix all day, but you're putting in the hard work and making a positive change. Keep it up.