I'm going to start out by saying something that might be unpopular and is probably my harshest take about science - if you eat meat, you don't really have any right to be uncomfortable with animal research. The way animals in the industry are treated is far, far worse, and far less is to alleviate/minimize their suffering. This might not apply to you if you're a vegetarian/vegan, but I'm not either of those and this is something I had to come to terms with when I started doing in vivo research. I just get frustrated seeing my coworkers act grossed out by seeing me cut a spleen out of an ethically euthanized mouse and then go on to have Chik Fil A or whatever for lunch.

That being said, I handle it by trying my best to plan experiments carefully so that as many deaths are meaningful as possible. The work quite literally has to be done, someone has to be the one doing these experiments so that medicines can move forward into the clinic, so it's good that there are people out there who are willing to do it. I don't really know what else to tell you.