At level 28 I stopped absorbing the souls of dragons when I killed them. Nothing happens. I guess this means I cannot complete Dragonborn.

Unclemike

Do you also have the Unofficial Dragonborn Patch installed (separate from the Unofficial Skyrim Patch)?

If not, install it. One of its fixes is:

Dragonborn's changes to DragonActorScript.psc have now been properly merged with the fixes done in the USKP. Dragon soul absorbtion is now working 100% correctly.

According to the Unofficial Dragonborn Patch's mod description, the load order should be like this:

Skyrim.esm
Update.esm
Dawnguard.esm
Hearthfires.esm
Dragonborn.esm
HighResTexturePack01.esp
HighResTexturePack02.esp
HighResTexturePack03.esp
Unofficial Skyrim Patch.esp
Unofficial Dawnguard Patch.esp
Unofficial Hearthfire Patch.esp
Unofficial Dragonborn Patch.esp
Unofficial High Resolution Patch.esp

Also as a reply to this answer, you shouldn't load Dragonborn after USKP, as it could undo the fixes of USKP. If unsure, just let BOSS take care of the load order.

Just as a note for future reference, once version 2.0 of all of our patches are released, it's going to be expected that Dragonborn will load after the USKP due to the new way the files are being handled.

BOSS should be able to take care of it either way, but just so you're aware.

It's not true that "Dragonborn changes the dragonactorscript". I've never had any problem with Dragonborn as to absorbing dragon souls. The problem comes from elsewhere. Do no spread false news, please.