Is it possible to be too empathetic?!

I know this sounds ridiculous, but I need help being less empathetic. Is that even a thing?

I'm now in my second week of Nursing school and we're just learning the foundations of Nursing and one of the topics is basically teaching us, or even reminding us to be emphatic.

My problem however is the opposite, ever since I can remember I've been emphatic almost to a fault. It sounds silly but I can just really feel what others are feeling so strongly and in turn I can get..upset..overwhelmed(?) very easily.

For example - my dad was in the hospital having a check up on a recent surgery and since it was going to be awhile my boyfriend and I went down to the gift shop to get a snack. While we were sitting at a table eating a nurse walked by and she was wheeling out an elderly woman. The elderly woman was rambling and seemed so scared and she was crying, meanwhile the elderly womans daughter was also crying and trying to reassure her mother that she was okay and they were just transferring to another hospital or something and just watching them wisk by us was to much and I started to cry for the women. Seriously as they walked by it was like I was hit by this heavy wall of their emotions and I can just feel it like it was happening to me..it's hard to describe. I could go on and on with examples but I wont, but even things less upsetting can still set me off haha.

I feel like I sound crazy but I would love some advice if anyone else has every experienced anything like this. I start my clinicals in a few weeks and I want to be able to keep it together when something upsetting happens so people take me seriously and I don't look like I'm unstable haha ugh.

Thanks for any advice!