The difference in meaning is that with this construction one tries something to see what the result will be, i.e. tries to see whether there will be any success, whereas with `try to verb', the idea is that the action one tried might not have even have been completed. Thus, with infinitive the meaning is `I tried to get a shot (but wasn't able to get one)' while the meaning with AVP might be `I tried getting shots (but they were ineffective for my medical condition.)