Is anybody else like this? My mom is annoyed by it!?

I just got back from a 3 minute walk because my park is filled full of people! Usually since it's summer, I walk my dog 2 times a day, usually about 2 or more miles each, and I love it when im the only one there, or theres not very many others. My town is small, about 3,000 people and as you can imagine we all know each others buisness >.< (I sometimes really hate my town) Theres a certain dirt path I always walk on because its off the side from the park, and not very many people walk on it. This time there was some people from my age group on it, then I went down the other side and theres a play production going on, so I went home. I hate it when people watch me walk my dog, especially if they are really close, then I tend to get made fun of. So in short, I usually stay away from others in public places where I want to be alone. My mother tells me that I will be like my cousin (really bad anxiety issues and wont even attend school) if I don't deal with it. I don't see my problem here with wanting to be away from others for an hour withought being bothered. Is anybody else like this? Or am I just being silly?

O and I have been made fun of one other time this happend, that's why I started to avoid people at the park when im on a walk. I don't mind running into others when im not on a walk, then im just fine. Except at this one gas station, when everybody in my school hangs out, I usually get some kind of sweet thing there like once every two weeks, then im afraid of being laughed at because of my weight...... if it helps im 16

sorry about the length :P