There is a difference in usage with the pedal immediately up after sign and the standard pedal up sign. And it can be ambiguous and difficult to tell the difference.
In my experience, the pedal immediately up after indication will be printed slightly to the right of the notes, as shown in the MBC2015 example 29.10.1-3 (d). In this example, the pianist would indeed lift the pedal in measure 3 after the right hand chord is struck. (Which is also why the pedal indication is placed in the right-hand line in the braille.)
It helps to have an understanding of how the music would be played and how the pedaling would affect the sound. If you're truly confounded, it would be advantageous to enlist the help of a pianist to find out how they would interpret the pedaling indications.
I just did a webinar on pedaling last month for the Music Monday series. Check it out in the archives.
As to the specifics of the piece you're working on, I'd have to see print in order to advise whether the standard pedal up would be sufficient or if it would require the use of the special signs.