Combine :after with :hover

in scss

&::after{
content: url(images/RelativeProjectsArr.png);
margin-left:30px;
}

&:hover{
    background-color:$turkiz;
    color:#e5e7ef;

    &::after{
    content: url(images/RelativeProjectsArrHover.png);
    }
}

Just append :after to your #alertlist li:hover selector the same way you do with your #alertlist li.selected selector:

#alertlist li.selected:after, #alertlist li:hover:after
{
    position:absolute;
    top: 0;
    right:-10px;
    bottom:0;

    border-top: 10px solid transparent;
    border-bottom: 10px solid transparent;
    border-left: 10px solid #303030;
    content: "";
}

 #alertlist li:hover:after,#alertlist li.selected:after
{
    position:absolute;
    top: 0;
    right:-10px;
    bottom:0;

    border-top: 10px solid transparent;
    border-bottom: 10px solid transparent;
    border-left: 10px solid #303030;
    content: "";
}​

jsFiddle Link