I've had the same problem for years. When I go on the treadmill at home, my mom mocks me and goes "you need to run faster."
When I go for walks, it's always at night because I don't want people to see me. I'm risking my safety to save myself from embarrassment :/ I've already encountered a bear and a vicious dog.
And the only gym I can go to is the one on an Air Force Base because it's free.... and, needless to say, the people there are usually really fit men. It's intimidating and embarrassing as ****.
However, recently, I had a pep talk with myself. I said "April, yeah, you're big now. And yeah, it's embarrassing to have people watching you exercise. But it'll be far more embarrassing to deal with this your entire life than to deal with a few months of people watching you."
So... just try to tell yourself that the end result is worth the pain.
Remember: "tough times don't last, tough people do"