Now it is also completely possible, as you suggested, that the interior brick is the load bearing structure. Now you have to remember when this house was built. Synthetic materails were not a common back in the early 1900’s. It is unlikley that the house has insulation in the walls. A common practice of that time was to actually build a double or even triple wythe wall system. A wythe is basically a line of bricks. In a multiple wythe system a wall of bricks is laid, an air space is left, and then another wall is constructed. This achieves a better system of insulation than just one brick wall. It is a similar idea to a double pane window. This form of insulation works pretty well. You will often get better and more consistent insulation from this version then you would from pourly placed synthetic insulation in a modern house.

There are companies you can hire to come out and assess the insulation properties of a building. I would imagine that any energy savings you might find by doing this would quickly be eaten by the costs. The other suggestion I would make is going to the local jurisdiction and obtaining a copy of the plans. I am not sure how large of a town you are in, but assuming the house was in some local jurisdiction when it was built, it probably needed a building permit. This means there should be plans on file (assuming they were not lost, stolen, distroyed, etc.). If there are plans it would show the structure of the walls, and should show the insulation as well. That is your best bet. Good luck.