A student pilot reported they turned crosswind to follow traffic as instructed by Tower but they turned behind the wrong aircraft resulting in a NMAC with other traffic in the pattern.

Narrative

During departure off of Runway XX to stay in the pattern for left traffic; ATC instructions were to extend upwind 1 mile and turn to follow incoming traffic for the pattern. After extending and when 1 mile away from the airport; ATC asked if I had traffic in sight and said that they were 'over [Location]'. When I looked off my left wingtip traffic was passing me and they were over the electrical plant called [Location]. I announced to tower that I had 'traffic in sight and turning crosswind'. Once established on my crosswind heading; the ATC controller then asked me if I had traffic at my 11:00 in sight. I responded negative and they instructed me to turn right. I turned right and during my turn saw the traffic pass by me. I reported this traffic in sight and turned back to be behind them after they had passed me. I had originally made my turn to crosswind when abeam the wrong traffic. I did not know that there were two airplanes that were near the Plant and it was not clear that I was supposed to turn after the second. I had made it clear to tower that I had traffic in sight and was starting my turn to crosswind because I was abeam the traffic I saw. When I announced my turn; tower did not give me any further instructions so I had no doubt that I was looking at the correct traffic. I feel that this could've been avoided if ATC advised me when I had announced that I was turning to not make my turn because I was looking at the wrong airplane. In the future; I will prevent this from happening again by making sure that I am aware of every airplane in and entering the traffic pattern. When told traffic advisories; I will ask further questions to clarify that I am looking at the correct traffic to follow.