"going through a list" is correct and usable in written English.
You can use it when you want to refer to examining or reviewing a list of items. For example, "I'm going through the checklist of supplies before we leave for the camping trip."
Going through a list of substances approved by the US Food and Drug Administration, the scientists found that vitamin B2 was a good candidate for lasing.
"Eclectic, I can't stand robotic, feeble – whether psychologists or just ordinary – people, if I think they are just going through a list of check points.
Once, when her mother was going through a list of after-school activities in front of acquaintances, the girl snapped: "That's one that I'm doing because you like it!" But mostly Asunta seemed happy.
And that conversation should involve going through a list of things such as, on a scale of one to 10, how far do you feel the woman's role is in the home, or how comfortable would you feel if your wife earned more, or what do you think is an acceptable amount of time to spend together?
Then they assess the situation, going through a list of other possible diagnoses, usually in order of most likely to least likely.
Lemaitre particularly emphasized the inbox, which he said is "really the place where the social media team is doing their day-to-day work," going through a list of social media mentions and either responding, noting that they don't need a response, or assigning them to different team members.
If you went through a list of them it would be like reading a medical encyclopaedia.
I just don't think it's useful to go through a list of that.
Troyanskaya then went through a list of other projects, at whirlwind speed.
One week, they had to go through a list of famous people and determine whether they were dead or alive.
He goes through a list of ministers, many of them former followers: "A time-server, a pathetic figure, a mere clerk, ambitious, weak".
