Will I lose weight like this?

I'm 13 and I'm overweight so my doctor said I need to lose some weight to get healthier and it will improve my breathing and happiness. So I have been eating well lately, alot of broccoli,artichokes,protein. But the only thing I haven't really done yet is excersize, there's a gym where I live that you can use the gym at 13 years old so I could go there all the time. Will I lose weight like this? Thanks