[Nagoyankee]

With drawings (paintings), we don't use the verb 作る. We use 描く（かく）.

私がその絵を描きました。 would be the most natural way of saying it.

You cannot say 私作. In Japanese, no sentence can be written in kanji alone.
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The Japanese particles are as important as 'word order' in European languages. Patience is the key.