The Schwarzschild solution is a static spherically symmetric metric. But I wanted to know that how would the space-time interval look in a Non-Static case. I tried to work it out and got $$ds²= Bdt² - Cdtdr - Adr² - r²dΩ²$$ Where $A,B,C$ are functions if $r$ and $t$. Being an amateur I am not sure whether this is correct.
While Qmechanic's answer is not incorrect, I think it is misleading and misses the point of the question.
First, there is the well-known "Vaidya metric", which is a simple generalization of Schwarzschild to achieve a non-static spherically symmetric spacetime. Of course, in agreement with Birkhoff's theorem, this is also a non-empty (non-vacuum) spacetime — but the OP never restricted to vacuum solutions.
Second, the question strikes me as being more immediately about the general form of a spherically symmetric metric. There's a nice treatment given by Schutz in his chapter 10.1, which is also mostly reproduced here, as well as chapter 23.2 and box 23.3 of MTW. The answer is that yes, a spherically symmetric metric can generally be put in the form given by the OP's equation. But it's also worth pointing out that the $dt\, dr$ term can be eliminated by redefining $t$ by a linear combination of $t$ and $r$ involving $B$ and $C$ (as MTW explain).