Help me lose weight, please?

So, I'm 15, 5'6", and I weigh 162 pounds. I know, it says my BMI isn't healthy and I'm obese, but my doctor always says I'm healthy weight. I am kind of muscular if that accounts for any of the pounds, but I know that I do still have fat on my body. I also eat healthy; fruits, vegetables, meats, dairy, water...but I also eat junk food; soda, chips, items with lots of sugar, etc. I just want to lose preferably 20 pounds by the end of the year, and at least 5-10 before I go back to school in September. Will running 5 days a week for at least 20 minutes help me accomplish that? What are some other exercises that would help with that too? And don't say swimming, even though I would love to go..because my dad won't let us get a pool and I don't really know anyone with one. :/ But thank you for any tips you can give me! :D