I would not say it is grammatically wrong.
However, the first clause will sound more natural if you use ばかりなので instead of から, as was pointed out by Brian.
Also, we usually describe レベル not as being 下手 or 上手, but as being 高い or 低い. (I guess this goes the same for the English word 'level'. You would not normally say a good level or bad level, but say a high level or low level, right?)
Therefore, the second clause can be 私の日本語のレベルはとても低いです. Another natural way of saying this is 私の日本語はとても下手です (= I am very poor at Japanese).
So the whole sentence could be paraphrased into: