Is this goal possible? I need tips and ideas too?

Hi! I am a female 5'7" i weigh *sighs* 158 lbs and i am 14 i am going to a water park on the 6th of july and amusement park on the 13th and i would like to loose 5-10 (hopefully 10) b4 the sixth and defiantly 10-15 b4 the 13th. Is that a reasonable goal? I know there is no magic pill and it will take a lot of hard work but i am up for the challenge and willing to work for the results. Anyway I have cut my carb intake substantially but not dagnegously. I am a vegetarian which makes that hard but i do it and i am quite active too (mostly in construction work this summer) Anyway we have a gym membership but it is hard to get my mom to take me. and i cant drive (leagly) :) we have a tredmill at home i live in the south so u cant really work out out side. I was looking for some tips exxercise ideas and eating tips. I mostly wanna slip down in my thighs and stomach :) thank you!!!