All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to cure you and increase your zeal to do good deeds.
There is no doubt that Allaah ordained the Muslim woman to wear the Hijab, so she must abide by it and she is not permitted to be negligent about it in any case. In fact, there is no specific dress for the Hijab, but it has some particular characteristics that must be fulfilled, among which is to cover the whole body, and the scholars differed in opinion in regard to covering the face. For more benefit, please refer to Fataawa 83702 and 83033.
Therefore, it is not permissible for you to wear the dress that was prescribed for you (by your friends) when you go out or when you are in the presence of non-Mahram men because it does not cover your body. In addition to this, Jumu’ah (the Friday prayer) is not an obligation on you; so how come you miss an obligation and do prohibition in order to do something that is not an obligation?
Moreover, if you want to listen to the Khutbah (the Friday speech) and gain religious knowledge, then this does not necessitate you to go out of the home, because it is possible to achieve this through the mass media or through the Internet and the like.
Of course, what your female friends said to you, like wearing short and open dresses is not advice at all; rather, it is like cheating. Indeed, the difficulty is removed in the Sharee’ah but this is when there is really a difficulty which is not present in your case. Attending the Friday prayer is not an obligation on you in principle, and you generally may wear special dress that covers your body without shaping it or making you feel warm.
In any case, if a woman is not able to wear the Hijab for some specific reasons, it is not permissible for her to go out unless she is in dire necessity, in which case, she would go out in order to do what she needs only and then return home, as the necessity is valued according to its proper value. However, if she does not have to go out, it is not permissible for her to go out, as the benefit of protecting one’s religion comes in priority.
Allaah Knows best.