Yes. You could say either:
I couldn't handle this situation without your help.
I couldn't handle this situation with no help.
In the second sentence, you could say "without help" or "with no help" interchangeably. "Without help" seems slightly more correct to me because "couldn't...with no" seems like a confusing number of negatives for one sentence. However I think that's just my personal preference; it is probably technically correct either way.
In the first sentence, with the article "your", you can only use "without".