Horton finished just .73 of a second behind Sun in a nail biter, but on the medal podium, the Olympic champion refused to stand with first-placed Sun, nor shake his hand.
Sun will appear at the Court of Arbitration for Sport (CAS) in September, but controversially, he was cleared to compete in the race. Sun, who is a three-time olympic champion, will answer to charges of allegedly smashing vials of his blood with a hammer.
Following the race, Horton spoke to media.
"Frustration is probably it," he said after his second-placed finished. "I think you know in what respect.
"I think you know what the rivalry is like.
"His actions and how it has been handled speak louder than anything I will ever say."
Sun later responded, accusing Horton of being disrespectful.
"I was aware that the Australian athlete had dissatisfaction and personal feelings towards me," he said at the post-race press conference.
"It was unfortunate because disrespecting me is okay but disrespecting China was very unfortunate and I felt sorry about that."
It's not the first time Horton has taken a swing at Sun. At the rio games, he labelled Sun a "drug cheat" before pipping him in the 400m freestyle race.
In 2014, Sun served a three-month doping ban. However, more recently, he is accused of objecting to an out-of-competition test last September at a home visit. Vials of blood were then allegedly destroyed by a hammer.
The World Anti-Doping agency lodged an appeal to the CAS following FINA's decision not to punish Sun on the basis that testers had not shown adequate identification.