Blown in insulation is one of the worst things you can do in brick faced houses - in fact, I was just reading an article on the thermodynamics of that very subject earlier today for a historic house rehabilitation design. Here is a more simplified article that discusses some of the problems with insulating brick houses -
The problem with brick houses, excluding modern ones with a positive vapor barrier and ventilation gap behind the brick, is they absorb moisture, then release it to the wall cavity. Putting anything organic in there is inviting mold and rot in short order. In addition, insulating the cavity reduces the amount of heat escaping the house, hence there is less drying on the backside of the bricks, which increases freeze-thaw damage on the bricks, and increases rot/corrosion for any beams or headers or such that are in the wall or supported on the wall.
IF properly done, closed-cell anti-fungal treated foam-in-place insulation can be used AFTER providing the correct interior ventilation provisions. This in another one of the cases where more is not necessarily better - full wall cavity insulation can cause significant damage to the bricks, leading to total breakdown, and inthe case of solid load-bearing brick walls, total wall collapse. There have been several buildigns in New York and Massachusetts with substantial wall failure attributed to insulation resulting in brick failure or supported beam or header failure.
The thermodynamics and hygrometrics (heat and moisture factors) are much too complicated to get into here - you can google the phrase - insulating brick walls - for articles on the issue - concentrate on the professional ones from architects and building associations and the foam insualtion manufacturers, because there are some out there who recommend cellulose, shredded newspaper, and so forth behind brick, which is a big no-no. Ditto for stone, by the way.
I hate to say it, but the current recommendation is to use exterior insulation like EIFS or board insulation under stucco or gunite or a metal facade, not interior wall insulation - which destroys the brick appearance of course.
Suffice it to say, before going ahead with this, consult an architect certified in building insulation systems to assess your situation and make recommendations.