When I hear the "woman voice" say this, it makes me second guess what I hear.
Why is 'I was thinking about my new work' not allowed? It seems that often when a possessive determiner is omitted in Polish one can still translate it as such, in situations where it would be logical given the meaning of the sentence. This is the case for many of the questions here, where sometimes it is even the suggested answer. Why is it different here?
Well, it's not that clear to me that it's "my new work", it's just new work (about searching for a new work, I would expect), but I guess that it does make sense and there's no harm in adding. Mostly the sentences omitting the pronouns refer to family or some objects that the subject most probably owns. Here it's a bit more of an interpretation. But alright, added.