The main difference in usage is between physical pain and emotional pain. "I am in pain" suggests there is ongoing pain, usually physical. "I am hurting" suggests there is ongoing pain, usually emotional.
This is an example of sense 2b the Merriam-Webster Learner's Dictionary:
2 a [+ object] : to make (someone) sad or upset : to cause (someone) to suffer emotionally
- Their lack of interest in her work hurt her deeply.
- You're only hurting yourself by holding a grudge against them.
- It hurt me to see her go.
b [no object] : to feel emotional pain or distress
- My sister has really been hurting [=has been very upset and unhappy] since her boyfriend left her.
And as for whether it's "slangy", here's a quote from a press conference Barack Obama gave in Nov 2014:
... there are still a lot of folks out there who are anxious and are hurting and are having trouble making ends meet, or are worried about their children’s future. [source]
There are hundreds more examples on www.americanrhetoric.com of speeches and interviews with similar examples of many different people using that word the same way.