The Kansas City Chiefs star gushed about his Feb. 22 visit to see his girlfriend on the latest episode of his "New Heights" podcast ... talking about it all with his brother, Jason Kelce, for around 15 minutes.

He spoke about the huge amount of media attention he received -- noting that cameras surrounded him the second he touched down at the airport.

"You're like the Beatles," Jason joked on pod.

Then Travis got into breaking down his zoo date with Swift ... explaining in great detail about all the fun he had checking out the animals with his boo.

Travis said he got to pet several creatures -- including a red panda -- and fed some, too. He did say, though, that photogs circled over their heads the entire time.

"They helicoptered us," Travis said. "Well, not us -- Taylor. This all because Taylor is the biggest and best thing possible."

Travis also had a ton of kind words for the fans at Taylor's show -- explaining that he thought the Sydney crowd was louder than the one he experienced in Argentina ... something he didn't seem to believe could be possible.

"Taylor's very fond of performing in Australia," Travis added.

The guys also talked about a whole lot more on the pod -- including Jason's retirement from the Eagles ... which the elder Kelce said ultimately came down to he wasn't sure if his body would hold up to the rigors of the NFL season any longer.

At one point, though, when reflecting on the end of Jason's career, Travis began to cry.