Yes, lupus could have developed in the last 5 weeks. All illnesses have a starting point, and just because your RA tests were negative, and also didn't show up anything pointing directly at lupus, it doesn't mean that it wasn't there.
Bearing this in mind, lots of painstaking tests need to be carried out before you are diagnosed within any one of the lupus groups. Quite a few of the things you mentioned "could" have a bearing on a lupus diagnosis. You need to be referred to a lupus specialist if you feel that you are showing symptoms of lupus.
In the meantime if you need any help, you have certainly come to the best place here. You will get the support you need. All of us have different stories to tell about our diagnosis, our subsequent treatment and so on.
The thing is I personally am not medically trained so I would not dream of making a guess. I have had SLE for over 30 years and I only share my own experiences of living with lupus and learning more about it.
Just one thing. If it is possible could you change your doctor? It doesn't matter what you feel is wrong with you and what eventually is proven to be wrong with you, you should be extended the courtesy of being taken seriously. The emotional issues of having any type of illness need to be taken into account, you need help and this doctor needs to know this.