You ask "with voldy murdering his mom and not using the horcrux making spell?". The answer was provided by Dumbledore (emphasis mine):

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building. ...” [ Deathly Hallows, Dumbledore finally explaining to Snape the full story as Harry is observing from Snape's memory ]

So, there were two events that happened to make Harry a "Horcrux":

• Avada Kedavra, when bouncing off of Lily's protective magic around Harry, hit Voldemort himself instead, and ripped off a part of his soul.

• Once his body was dead/gone/destroyed from Avada Kedavra, that ripped off soul piece tried to find a new host, and Harry was the only host available.

You ask "with voldy murdering his mom and not using the horcrux making spell?". The answer was provided by Dumbledore (emphasis mine):

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building. ...” [ Deathly Hallows, Dumbledore finally explaining to Snape the full story as Harry is observing from Snape's memory ]

So, there were two events that happened to make Harry a "Horcrux" (quotes are there on purpose - see Slytheincess' answer):

• Avada Kedavra, when bouncing off of Lily's protective magic around Harry, hit Voldemort himself instead, and ripped off a part of his soul.

• Once his body was dead/gone/destroyed from Avada Kedavra, that ripped off soul piece tried to find a new host, and Harry was the only host available.

You ask "with voldy murdering his mom and not using the horcrux making spell?". The answer was provided by Dumbledore (emphasis mine):

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building. ...” [ Deathly Hallows, Dumbledore finally explaining to Snape the full story as Harry is observing from Snape's memory ]

So, there were two events that happened to make Harry a Horcrux:

• Avada Kedavra, when bouncing off of Lily's protective magic around Harry, hit Voldemort himself instead, and ripped off a part of his soul.

• Once his body was dead/gone/destroyed from Avada Kedavra, that ripped off soul piece tried to find a new host, and Harry was the only host available.

You ask "with voldy murdering his mom and not using the horcrux making spell?". The answer was provided by Dumbledore (emphasis mine):

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself onto the only living soul left in that collapsed building. ...” [ Deathly Hallows, Dumbledore finally explaining to Snape the full story as Harry is observing from Snape's memory ]

So, there were two events that happened to make Harry a "Horcrux":

• Avada Kedavra, when bouncing off of Lily's protective magic around Harry, hit Voldemort himself instead, and ripped off a part of his soul.

• Once his body was dead/gone/destroyed from Avada Kedavra, that ripped off soul piece tried to find a new host, and Harry was the only host available.