I'm on your side but I can understand your parents concerns about anorexia. I've had several family members that had bouts with the problem. If you know that calorie counting can become excessive don't count calories.
I'm still amazed at myself that I have been suceeding as it has been many years since I have done anything but eat whatever I wanted and continually gain until I was over 250 LBS. When I started this I did so half heartedly. I cut certain items from my life like sweets and salty snacks. After a short time I wanted to do more so I started walking a little everyday. Next was attempts to increase the amount of water I was drinking as the only beverage that ever crossed my lips was diet soda. Then I decided to eat whole foods more often which meant eggs, yogurt, baby carrots, cucumbers, inexpensive frozen vegetables, meats like chicken, hamburger, pork, beef, bananas, apple, berries, almonds. I also started paying attention to portion sizes. I've done a lot of research online regarding different food plans. It's free. I also found wisdom support and encouragement on line as my family isn't the most supportive. But thats OK. Because I am the one on this journey.
What I'm trying to say is pick a couple of bad habits you have and set out to change them and go from there. If your parents see you not going to extremes they will probably be more supportive. I'm guessing there are some things that your folks buy that are OK diet wise. MY adult children like to go grocery shopping with me when they are around so they can encourage me to buy things they want. Your folks would probably be OK with that too.
As some one mentioned UTUBE has free exercise videos. I also did quite a bit of my diet research there. Fom learning how to make smooties, researching various plans, watching weight loss blogs of people who were willing to share their journeys.
I'm not smart about posting links but if you search here regarding the stages of change you will find an excellent post where someone did post a link. It would be good to read through and figure out what stage you are in. Hope you can puzzle through this and make some healthy choices.

