Now I'm not going to say that there aren't people judging you. The harsh reality is that there are in fact some people who are going to judge you for not moving as much weight as them or (possibly) using poor form. Now that that's out of the way here's the good side of this post:
1: You pay for the gym just like everyone else, and their money/time is not worth any more than yours which means they're no less deserving of the equipment.
2: Any person who's actually willing to judge another person who's actively attempting to better themselves is not a person who's opinion should matter in the slightest, in short: They're assholes and they're only in the gym because they're insecure about themselves.
3: Every person starts somewhere, and I'm sure you've heard this time and time again, but allow me to elaborate. When my training partner first started lifting he actually trapped himself under an empty barbell doing bench press, he had to do the "roll of shame" (it's really not shameful everyone who lifts has done it at some point) to get the barbell off of him and go back to doing other exercises until he was strong enough to lift the bar. Here's the important part, last month he bench pressed 260 pounds and he was only able to do that because when he first started he realized that the goal of lifting is not "I must lift more than the person beside me" and rather is "I must lift more than I could last week/month/year." You're not competing against the other people in your gym, you're competing against yourself from the past.
4: Form is far FAR more important than weight, any lifter worth their salt will tell you that when they walk into the gym and see the guy who's got 315 on the bar bench pressing quarter or half reps he's immediately judged more than the girl next to him who's struggling to bench an empty barbell but she's touching her chest on every rep, keeping her elbows tucked, and controlling her breathing. The reason for this is that the girl in this scenario is obviously trying to better herself; she's using good form to protect herself from injury, she's started at a weight she can handle so that she can teach her muscles the movements that will allow her to healthily build strength, and she's completing her reps so that she gets the full benefit of the movement. The guy on the other hand is judged mercilessly because he's trying to show off and embarrassing himself in the process.
I'm sure this rambled more than a bit but I hope you get what I'm trying to say. Lifting in any capacity is 90% a mental activity and 10% physical, you have to look at the gym from a different perspective and understand that you're there to better yourself for yourself, and no one else. The road block that you have now (overcoming your fear of the free weights section) will seem silly in a few months time when you're looking back and instead you'll be here asking how to get through the mental barrier of adding your first 45s to the bar.
Just to wrap things up: Watch a few YouTube videos, and ask around if you have any concerns about your form, go to the gym and lift using your good form, and try every day to beat yourself from yesterday. Pretty soon you'll forget about the other people in the gym because you'll be too busy competing against and beating your own PRs and that's really all that matters.