Alternating the two medicines is fine, but piggybacking them, as Samantha suggested (IBU, then two hours, TYL, then two hours, IBU etc., ) is only recommended for a high fever that will not break, not for everyday pain. For the pain of a cut or other everyday-type occurance (twisted ankle, etc.) this would be overmedicating. However, if you started with Tyl/Acetamenophin and would like to switch to Motrin (Ibuprofen, Advil, all the same meds) after the first four hours, there is no problem with doing that.
I would also change the bandaid every 12 hours or so. On a finger there is no pain/drama about removing the bandage and it will heal faster if you change it and apply fresh ointment on a regular basis. The Neosporin I use has a mild topical pain reliever in it which will help with the discomfort and is perfectly safe when used with oral pain relievers like IBU and Acetamenophin.
Lots of cuddles and kisses will help too!