Air carrier First Officer reported receiving an obstacle alert on approach to LGA when they descended below charted altitude because they had a wrong altimeter setting selected.

Narrative

I was pilot monitoring on the RNAV 31 into LGA. After being vectored onto the final approach course the Captain and I were struggling to make out the field with the unfamiliarity of coming into LGA from this direction. Once I made the field; I noticed 4 red on the PAPI's and communicated we were low and recognized it was due to an improper altimeter setting. While communicating we got an 'obstacle' alert and immediately executed the escape maneuver and went around. After clean up we verified with ATC the new ATIS and altimeter setting; set up for another approach and conducted it without any issue.The altimeter setting we had in was 29.95 given by approach for the Philly area. Captain and I talked about how this was a threat because LGA was reporting much lower; 29.77. Once changing over to LGA Approach we were not given a new altimeter setting; but noticed aircraft were being handed off to a Final Approach Controller when crossing the field on the Proud2 arrival and expected the new altimeter setting to be given then. Our Controller then took over vectoring arrivals onto the final approach course and that frequency change never came. It was bumpy and the winds aloft were causing the Controller to give us lots of heading changes as we were getting vectored around that I simply got task saturated and never went back to verifying the local altimeter setting prior to executing the approach.Suggestions: ATC should assist pilots and provide local altimeter settings when checking on with new areas.Add into the pilot monitoring flow for an approach to verify altimeter; as the last time this is done is going through FL180 on the descent checklist which in our case was far enough out we were still in Philadelphia's airspace.