Is the sentence correct?

Question

I am well succed in professional career and I have much prosperity.

Answer 1

No, "I am successful in my career, and this has brought me prosperity" is perhaps what you are trying to say.  You could say "professional career" although I don't see that it adds anything important.  The important thing is being successful, not that you are a professional, in this statement.You have prospered because you have been successful, although one can be successful yet not "prosper" in a financial sense, which is how prosper is typically employed. 

I have been quite successful in my career, my career as a professional, if it matters, but I would not say that I have become rich from it.  Riches were not the objective.  I prospered in the sense of gaining responsibilities and independence and the confidence of the clientele.  Those were my goals, so I can say I prospered, but not in a traditional (monetary) sense.  I did not suffer financially either, but I definitely did not become rich. I never tried to become rich, to be honest.

Answer 2

“Success” and “prosperity” are synonymous. Using them together isn’t good form.

The whole thought behind that sentence could be written:

“I am successful in my professional career.”

My personal writing style is always to say as much as possible with few words.

Answer 3

No.