One of the dolphins at Toshima in Japan has this. His nickname "Kaisou" means seaweed in Japanese. He has a severely twisted jaw. Underwater photographer and nature guide Nana Takanawa can tell you much much more about him as she dives with the pod on a daily basis. 

https://www.youtube.com/watch?v=JFVp_OLDp_I

This video shows his family but I can't identify him in it. There is a similar growth on the tail of the dolphin at 9:35.

Nana told me it disappears in the winter. 

If you can't contact her via Youtube, please send me a private message for contact details.　

Here's a photo:

http://tosimadiving.cocolog-nifty.com/blog/2013/06/post-39b5.html

P.S.

If you want to search in Japanese, the name is カイソウ and the word for dolphin is イルカ 

http://toshimadolphinproject.web.fc2.com/T021MS1.jpg

Simon, thanks so much for the info. I'll run the photo by the 

Thanks Simon for sharing this information.

P.S. I'm willing to "go between" if you have language difficulties but Nana Takanawa is effectively bilingual.

Head-on shot of Kaisou, when the growth was quite long. (if you can see Facebook)

Another shot from Nana Takanawa.

https://www.facebook.com/photo.php?fbid=986676038026224&set=a.267726529921182.87543.100000515114381&type=1&theater

HI Katherine,

Perhaps the skin lesion from the mouth of the dolphin can be a tumor or a possible case of fibropapilomatosis (fibropapiloma). In manaties from Florida, fibropapilomas can be observed on the skin. I hope this can help a bit. JJ

Since you don't have photos, it's difficult to know what the cause of the condition you mention. However, the video and photo from Simon seems to me to be stalked barnacles. They have been described in many cetaceans, and I've found in franciscanas (Pontoporia blainvillei) from my area. You can see a photo of it at https://flic.kr/p/rPR6qt