Your home meter gives current BG readings ( accurate to approx 15% or so depending on levels ). Your HbA1C gives a 3 month approximation. This is the figure your doc is normally interested in. The only problem with 3 month avg is it could mask lots of hypo's and highs to give a nice avg number. I you concentrate on your current levels and act accordingly, the HbA1C will look after itself.
The new HbA1c is in mmol/mol, the old way was in DCCT which gave it as a percentage and your home meter gives it in mmol/l. So for your last HbA1c it was 7.4% DCCT, 57 mmol/mol, which works out as an average of 9.2 on your home meter ( if you were testing constantly over that period)