i found the Gym to be a very weird place, like you i get embarrassed about running / working out near people as you feel bad when you see someone doing better than you,
i drummed up the courage to go and no one really notices you everyone is just doing their own thing, i like to get Netflix up on my phone when i'm on a treadmill / cross trainer and just go into my own little world, As Pipnina said walking is a great way to do it
Another thing i found really useful / interesting was counting calories using an app on my phone it was really eye opening to see what everything you ate adds upto and as long you burn more than you consume the weight will fly off