I found that "run-in" line on page 52. Dally is describing what happened between Tim Shepard and himself when he uses the term "run-in." Tim is the leader of another Greaser gang and is a friend of Dally's. The two of them respect each other, but don't always agree on courses of action. When Dally says that he had a "run-in" with Tim and "cracked some ribs" he is saying that he and Tim got into a little bit of an argument. The argument must have gotten heated and maybe some punches were exchanged. By saying "run-in" Dally is trying to downplay the seriousness of the encounter, argument, and injury.
As for "show," I couldn't find it on page 115. I found a reference to it on page 117. "If the fuzz show, you two beat it . . ." In that case the word means "arrive." Darry is saying that if the police arrive, get out of there fast.
I found another "show" reference on page 97. "I'm not going to show at the rumble tonight." Randy says that line and he means that he is not going to take part in the rumble. He is shortening "show up" to just "show."
Thanks! You are a real life saver. :)