That's OK. (My Hodgdon book indicates the rim is .378", and the case head immediately forward of the extractor groove is .375". Your book, and your ammo, are in the right ballpark).
Adjusting the dies up or down will make very little (probably *no*) difference to the size of the case head. If a fired case is swollen up quite a bit, the die will size it down (hopefully small enough so that it chambers into your rifle without resistance).
If you have an AR-15, you can break it open and remove the bolt carrier, and then feed a sized case into the chamber by hand - it ought to effortlessly go in, and once fully seated it ought to have a little bit of side play at the back end of the case. In a bolt action rifle, you can take out the bolt (and magazine) and do a similar "fit and wiggle" test.