Processing people's emotional distress

My best friend doesn't 'burden' me with her problems (when she's feeling low, upset etc) because she feels hurt when I don't react in a typical empathetic way.

This actually upsets me because I feel a whole part of her existence is being filtered out to avoid causing either of us harm, which makes me feel the friendship is less authentic.

For context - When I'm confronted with these situations, I believe I experience emotional/sensory overload which leads to shutdowns. I also believe that I may be feeling their emotions but not fully understanding what that emotional state is, which leads to distress. I also feel a sort of pressure to do/say the right thing, which is stressful but can also feel inauthentic. Most commonly I shutdown, but I have also had to flee the situation because it became so overwhelming, which makes me feel terrible, but I had to do it. An additional note is that I'm also very empathetic with my dog, and animals in general. Way more than humans.

I'd like to become better at dealing with negative emotions in order to strengthen our friendship, so I'd like to ask if anybody has had any luck at being more emotionally supportive for the people they care about. Gimme some examples Slight smile