When comparing your current prescription with your previous one you not only need the astigmatic correction but also the angle of the correction, together with the basic prescription for the distance lenses. Comparing prescriptions is complicated by the fact that different opticians use different conventions for describing the lens; as a sort of analogy, think of the distance from London to Manchester - you can define it as London to Birmingham PLUS Birmingham to Manchester OR London to Glasgow MINUS Manchester to Glasgow. Both give the same result but look quite different on paper.
You also need to get someone to measure the distance you hold a book from your face, the distance you sit from your monitor at work and the distance you sit from your monitor at home - giving the optician these measurements will enable him to calculate exactly what lenses you need.
Incidentally, when I was working my employer gave me an annual eye test and a pair of glasses specifically designed for screen use at work; yours might also do this for health and safety reasons. A dozen years after retirement I still use a pair of specs specifically for computer use at home.