First of all, I want to tell you that Portuguese and Georgian has a lot in common.
Let's talk about the sentences you wrote:
1) I am afraid of Dogs/ I fear Dogs.
In Georgian we would say that like: მე მეშინია ძაღლების or ძაღლების მეშინია. | me meshinia dzaghlebis or dzaghlebis meshinia.
But in Portuguese we say: Eu tenho medo de cachorro, which literally means: I have fear of dogs. So The third version in Georgian could be the same like in Portuguese : ძაღლების შიში მაქვს. |dzaghlebis shishi makvs (makvs- I have | shishi -fear | dzaghlebis - of dogs)
2) I am worried about this problem - Eu me preocupo com esse problema.
We have two options to say the sentence:
a) მე ვღელავ ამ პრობლემაზე | me vghelav am p'roblemaze.
b) მე ვღელავ ამ პრობლემასთან დაკავშირებით | me vghelav am p'roblemastan dak'avshirebit.
[Both of the sentences expresses the same idea]
This problem worried me - Esse problema me preocupou
In Georgian, the sentence would be like that: ეს პრობლემა მაღელვებს | es p'roblema maghelvebs.
P.S As I saw Giorgi has used another verb to express the word "worry", so don't get confused- his sentences are CORRECT as well. The only difference is that "ვღელავ" means I worry, and "ვნერვიულობ" means "I am nervous about smth" :)