I am 62 and very recently sat with my mother while she died from sepsis. started having heart palpitations a week later. is this normal?

Grief: I'm glad you were able to be with your mother during her passing. Sepsis isn't contagious. The process of losing a loved one can and will change your physiology some, and these palpitations are fairly common. This might be a good time to cut back on caffeine / tobacco if you do these. If you start seriously losing your breath, or have more than five flip-flops per minute, get seen.