Well the reference to the window seems unique. I would assume that means that the wood around the window has expanded ( due to maybe temperature or humidity), causing it to keep the window from opening. When I think of something being swollen shut, I think of someone getting a black eye. Say someone got hit hard enough, or enough times, the skin around their eye would swell/expand so much that it would be "swollen shut."

This means that the frame has enlarged in size, perhaps due to moisture, and because of this increase in size, the window cannot be opened. This is also a common phrase used with an eye. If a person is hit in the eye and the area around the eye swells in such a way that the eye cannot be opened, you say that it is "swollen shut".

It's very common in the United States in wooden houses. Wood is "hygroscopic." It swells in moist weather and it shrinks in dry weather. This causes problems in structures made of wood. A traditional window has a wooden frame that slides within a wooden groove. The window slides up and down to open and shut it. A pulley and sash weights counterbalance the weight of the window, so it moves up and down easily and stays in place. This only works if the window frame fits just right in the groove, not too loose and not too tight. In dry winter weather, the window becomes too loose. In damp spring and summer weather, it swells and gets too tight. It may get too tight to move. It is "swollen shut." Wooden windows are often "painted shut," too, when too many coats of paint are sloppily applied. Paint can get into the crack between the window and the frame and act like glue. And the sash cords can break so that you have to lift the full weight of the window--and it won't stay up and comes crashing down again unless you jam a stick in it to hold it open. It takes good maintenance to keep the old windows working and it is almost normal to have many of them stuck shut in old houses. (Like many homeowners, in order to save energy and have windows that open and close easily, we have had all of our windows replaced with vinyl windows and double-paned glass. This is usual on new construction in colder climates).

stuck window, candle wax helps window glide better on their tracks.