When you say, "pulling away from the house", could you elaborate a bit? Is the veneer moving away from the back-up wall? Is it deflecting the supporting wood downward?
The brick should have proper ties back to the wall behind it. If not, then there is the potential for the veneer to unzip and fall over. Verification of ties is difficult, but can be done by cutting into the wall from the inside to allow inspection laterally within the (hopefully present) void space between wall and brick. There are also devices you can purchase that are small optical lenses at the end of flexible tube extensions that allow inspection in tight spaces.
As far as the vertical support, normally one tries to avoid supporting concrete, concrete block, or brick on wood. In fact it is denied by the IBC but as a residential house, there are provisions within the IRC that allow it.
Brick can arch so you could start at the inside and create a masonry in-fill between porch roof members to establish a rigid support for the brick above. Do this in small sections, allowing the brick to arch between its current supports, working your way outward towards the ends of the porch seems to me to be the best sequence....installing the lateral ties first, of course.
This can be tricky and difficult work, not to mention somewhat hazardous. If there's any question about it, I'd get some good contractors and an engineer to look at it.