[willy]

Where is the swelling you are talking about, is it only at the top where you took the pics?
Did you do as MJ said trying to flex the the transom applying leverage to the lower unit?
If you did and got no flex then I think you might be OK, but you still need to drill a couple of holes and check wood that comes out.
If it comes out OK you may have a simpler repair. There is a chance that is just filler that has deterioated. That filler may not have been put in there by the factory but may be bondo or the like put in to address the appearance by a previous owner.
If it is and all else is strong and DRY, you will be able to grind it out and cap it in fiberglass as Stinky did on his Baby V, check his post out he did a nice job and you will get an idea of what I mean.
If that transom flexes, or you get wet darker wood come out you need to do a transom job, and from the things I have heard there really is only one way to do it right, with lams of marine wood and glass or one of the new (cost prohibitive) structural foams some builders are using now.
Take a look at your motor bolts that go thru the transom, are they dimpled in from wood expanding and the bolts obviously not moving?
Are there cracks along the joints of the motor well or along any parts of where the transom meets any other walls?
Have you looked at the stringer knees where they come up and join the transom? If they are soft, if they have cracks running along where they join the wall of the transom you will have your answer because you will need to address them right away and do the transom at the same time. It would not be safe to operate the boat under those circumstances.