"To be honest it has really gotten to me, and I am trying to ...do something."
... it has really gotten to me, ... Has it got only one possible meaning or may be two or even more ?
It is sort of a phrase and I can't catch it.

The full quote from the interview: "To be honest it has really gotten to me, and I am trying to balance my own tears with having something to say that pushes the conversation forward."

Question

"To be honest it has really gotten to me, and I am trying to ...do something."
... it has really gotten to me, ...   Has it got only one possible meaning or may be two or even more ?
It is sort of a phrase and I can't catch it.

The full quote from the interview: "To be honest it has really gotten to me, and I am trying to balance my own tears with having something to say that pushes the conversation forward."

Answer

"It has (really) gotten to me" means that the situation has deeply affected the person's emotions/mental state/life/etc. For example:
"I never got to say goodbye to my dad. It still gets to me."

"Gets me" can also be used. However, this phrase can be used in both a positive and negative way. For example:
"The Dead Bird skit by Monty Python always gets me/gets me every time."
"It always gets me when/It gets me every time I see a small child crying."
"Gets me every time" is idiomatic and a little more common than "always gets me".