Even though you already have an answer, I'll just through this piece of information. It is never clear if he actually did die since it stated that he shot himself and was seen being taken to the hospital. However, he was seen teasing that he might actually kill himself on several occasions as shown in this article:
When one person warns, “Whatever happens to us, happens to you,” he
darkly responds, “So if I kill myself, you die too?”
On other occasions:
The episode dedicated to his tape, Alex also quits jazz band despite
his passion for playing the guitar and is later seen jumping into
Bryce’s pool, letting himself sink to the bottom before reality sets
in.
Also, the common sense is that he DID shot himself and it was not killed by Tyler. Take into consideration that Tyler was remembering the moment that Alex helped him and then took his picture out because he would spare him.
Some might argue that this moment was to show he killed Alex and removed him from the list, although that would be really bad storytelling taking into consideration the order of events. I might be wrong since I watched it quite some time ago, but I recall this order of events:
Alex is shot -> Tyler's Memory -> He removes the picture