Dear @kayijuka,
Welcome to the Wefugees Community and sorry for the late reply.
I assume your application for family reunification got rejected because the marriage took place after your wife was fleeing from her country of origin. In these cases, the family reunification for people with subsidiary protection is only granted in very exceptional cases.
Whether an asylum application in Germany is the best option for you or not is depending on many factors and it is hardly possible to give tailored advice on this here - especially without knowing your circumstances well. Other options to obtain a legal residence may be more promising for you. The "Make it in Germany" website can be useful to get a first overview regarding job and training opportunities in Germany, for instance.
Neverthelsess, looking for individual and professional support is definitely recommendable and even necessary from my point of view. Hiring a lawyer, as you already mentioned, could be one option. As a first step, you may also contact a counselling office. I made some research and learned that there are several organisations in Braunschweig and Wolfenbüttel offering confidential and free of charge services, i.e. the "Refugium Braunschweig" or the Caritas in Wolfenbüttel (just follow the links for the respective contact details).
In any case, please also don't hesitate to get back to us with any further questions.
All the best,
Meike