It took me 4 years of trying to start attending the classes at my gym regularly. The issues were similar to yours, but I also suffer from social anxiety, so apart from being uncomfortable, I was always on the brink of a panic attack. Sometimes I would attend a class a few weeks in a row, and then run away not to come back for months... so I can understand perfectly well how you're feeling.
Glad to hear you've decided to go, and I hope you enjoy the class and decide to come again and go to more!
But even if you don't like the experience, try to go again, for yourself - this is what helped me in the end. At some point I was just so unhappy about my weight and the way my body felt and looked that I thought, heck, I'm doing this, for myself.
A few hints I can think of...
do try to take a friend with you or even try to befriend someone at the gym (having someone with you really does help, especially if this person is in a similar situation as you!);
go to as many classes as you can one week and see how you like them and the instructors;
if you like the instructor, try more of their classes;
if you like the class, see if there is another one with a different instructor and decide whom you prefer;
pick classes with easier difficulty at first to make yourself comfortable with the equipment and routines (in my gym they have levels 1 to 4 and at first I started going to Step 1/2/3, which would become too overwhelming and too difficult and harder as the class progressed, so I was discouraged and disappointed; but I started doing much better in this class after attending a few Step 1 classes)
depending on your preference, you might like busier classes with more people attending, or ones that have lower attendance - try to figure out which ones have which, and then attend the ones you're more comfortable with
Good luck!