I can not take off my jacket

Even tho it's hot outside I just feel like I cant leave the house without it. My chest starts to itch every time I think leaving with out it. The kids at my school even gave me a nickname for that (at least that is what she told me). Its Pufi or Pufoaica. I dont mind it tho. Almost everyone i making fun of me for that. You know the wierd stares I get when its 20 celsius or more and I walk outside with that? Honestly I feel naked with out it. Its a part of me at this point ( I have been doing this for 3-4 years now ).