"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".