I think that your "estoy ocupada que" should rather be "estoy
preocupada por/porque"; otherwise, it should be "estoy ocupada
de/en/con". Both expressions have different meanings and different constructions, none with the subjunctive.
- Estoy preocupada por el niño. (I'm worried about the child.)
- Estoy preocupada porque el niño tiene fiebre. (I'm worried because the child has a fever.)
- Estoy ocupada de los niños de mi hermano. (I'm taking care of my brother's children.)
- Estoy ocupada con las labores de la casa. (I'm busy with the chores at home.)
- Estoy ocupada en hacer llamadas al servicio técnico. (I'm busy calling the technical support.)
However, if you say: "me preocupa que", "lo que me preocupa es que", "lo que más me preocupa es que"... then the subjunctive is necessary, if the subject of both verbs in the sentence is different (Check
this thread and
this one to see what I mean).
- Me preocupa que lleguemos tarde. (I'm worried that we'll arrive late.)
- Lo que me preocupa es que el niño se enferme. (What worries me is that the child will get sick.)
- Lo que más me preocupa es que pierdas el trabajo. (What worries me the most is that you may lose your job.)
The answer to your questions is yes. When you are stating this kind of own appreciation (lo que importa, lo que temo, lo que me preocupa...), you need the subjunctive (or its equivalent construction with the infinitive).
As for your first example, the construction would be much better with the infinitive, since it's only you in the sentence. Your second sentence is alright, since there is an impersonal and a third person.
Last note: "mas" means "but", and "
más" means "more".