That usage of overwhelmed is perfectly fine. We do not say "since two weeks", however, you say since + date/day. E.g. since February, since 2001, since 1st of July, etc. The most usual way to say what you mean is "For two weeks" or "For the last two weeks".
You would normally drop the "my" in your sentence, and say "overwhelmed by work" and you cannot say "busy by work", it should be busy with work, or at work, or busy working.