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The Welsh swimmer added 800m freestyle silver to her 400m freestyle medal after being beaten again by record-breaking American Katie Ledecky.
"I finally started believing in myself," Carlin told BBC Sport.
"I have been working with a sports psychologist on that side of things as well and not just the physical side."
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The 2014 Commonwealth and European 800m freestyle champion was beaten by Ledecky, who took nearly two seconds off her own world record to win nearly 12 seconds clear of Carlin.
The 19-year-old from the United States became the first woman since 1968 to do an Olympic cleansweep of the 200m, 400m and 800m freestyle titles to win her fourth gold medal of the Rio Games.
Carlin, who missed the London 2012 Games because of illness, celebrated her "incredible feeling" after years of upheaval after changing coaches and moving training bases to Bath under Dave McNulty's guidance.
"It has been tough," admitted the 24-year-old.
"I relocated to the Bath programme two years ago and changed coaches and change where I live.
"So to come away with a silver medal is an incredible feeling."
Carlin won the fifth Welsh silver of the 2016 Games in the pool just hours after cyclist Owain Doull won Wales' first gold in Rio in the team pursuit.
Carlin is just the second post-war Welsh athlete to win two medals at one Olympic Games - alongside double equestrian champion Richard Meade at Munich in 1972 - and becomes one of the most successful Welsh swimmers ever,
Irene Steer is the only Welsh female swimmer to win an Olympic title - in the 4x100m relay at the 1912 Games in Stockholm. David Davies has won two Olympic medals - a 1,500m bronze in 2004 and open water silver in 2008.
Carlin became the first Welsh female swimmer for 80 years to win two medals in one Commonwealth Games in 2010, then became the first Welsh female swimmer to win a Commonwealth title in 40 years when she struck gold in Glasgow two years ago.
Former double Olympic champion Rebecca Adlington praised Carlin's silver double at Rio and insists her success in Brazil has "written off" any disappointment from London 2012.
"The fact she has backed up silver in the 400m and come away with two silver medals at an Olympic Games is just fantastic, " said Adlington. "I think she will be over the moon."
Jazz Carlin has admitted her two Olympic silvers in Rio is after she "finally started believing" following advice from a sports psychologist.