"To not feel...still" is actually not a sentence. It is a subordinate clause because it has no subject. To answer your question, you can omit "standing" but the word "standing" does improve the sentence. Time is never still. It is always moving. However, it can "seem" still, or it can "feel" like it is standing still. It can also "feel still" but by adding "standing" you create a more colorful image: time is moving along and then all of a sudden stands still! The image is more vivid that way.

‘Time stood still’ can have various almost contradictory meanings. For example, you can use it to describe a situation where nothing is changing and life seems boring. Time stands still in the small town where I grew up. (Nothing ever changes) It can also convey a sense of shock. When I heard the news that my family died in the disaster, time stood still. (It was so overwhelming that it consumed me. It wasn’t just another normal event. It was something so important to me that it seemed to stopped time.) ‘Time standing still’ is a set phrase and can’t be broken up. ‘Totally’ is interesting here. It’s an intensifier that’s often used by the young and can sound very informal. ‘That new girl in class is totally a babe.’ (Said by a teenager to mean that she’s very attractive) ‘I’m totally over Formula One. I liked it for awhile but have lost all interest.’