I would avoid it.
First, DMSO causes everything that's sitting on your skin to get absorbed into your bloodstream (the wikipedia article about it is fairly thorough), to the point that it's actually a drug delivery system. Putting it onto your skin means that other things on your skin will get in as well. The skin acts as the first line of defense against the outside world.
According to the NY Times, in 1994, a woman who treated herself topically for pain with DMSO had the chemical metabolize into a nerve gas in her bloodstream:
The report theorized that DMSO, through the right combination of temperature, oxygen and blood chemicals, changed into dimethyl sulfone in Mrs. Ramirez's body and changed into a third chemical, dimethyl sulfate, in the syringe with her blood sample.
"The final, volatile product is extremely poisonous," the report said.
There have been some reported healing improvement on gastric ulcers in rats, viz. Naito et al in 1995:
DMSO and allopurinol significantly increased the collagen fiber proliferation index and the PAS-positive mucous score compared with controls. These results indicate that scavenging hydroxyl radicals or inhibiting xanthine oxidase enhances the quality but not the speed of gastric ulcer healing.
I could not find recent studies showing that DMSO was a useful healing agent, although it does appear to be used as a control in other wound healing studies, including those for PADMA 28 (Aslam et al, 2010, Barak et al, 2004); and for Caspase 8.
So, while it might do some good, it might also do some real harm. Another account in Discover stated that a doctor who supports the use of DMSO as a healing remedy, Stanley Jacob:
doubts that significant quantities of the suspect chemicals could have been produced from dmso. In fact, Jacob says, the Livermore scientists should never have allowed the Riverside coroner to release their report. It’s like that silliness with cold fusion, except this has the potential to hurt people, he says. His office has received dozens of calls from worried women being treated with dmso for interstitial cystitis. I just tell them the dimethyl sulfate theory is a chemical impossibility, says Jacob.
This same Dr. Jacob appears all over the dmso.org website, so he may or may not have a commercial interest in thinking that the chemical analysis in the Discover article is bogus.
In any event, as I said, I would avoid it.