It may help considerably, nor not much, depending on exactly what the issue is. I find that for interiors like that I haven't actually need to use shift much (but I don't have a lot of experience either), but the TS-E will have a lot less barrel distortion than most UWA lenses.
It might be for the types of shots you are doing that horizontal shift may actually be more valuable than vertical though (TS-E will do both simultaneously). I personally had a bit of a 'eureka' moment when shooting architecture a few months back when I realized I should also be considering horizontal shifts. Any time you are angling the lens either vertically or horizontally, you will create distortion that can be corrected using shift (if you have enough shift available. However, even with this you can get some strange perspective effects simply due to the UWA perspective.
An example shot that you are unhappy with may help us determine if a TS-E would do a lot better, but ultimately you may just have to rent one to see.