Thanks for posting your bottle.
In many cases, older does mean more valuable and perhaps more interesting. We would like this to be Civil War era but it is not.
Your bottle is machine made and we can date it fairly precisely. Such a precise date is not often the case. In Julian Toulouse's Bottle Makers and Their Marks, he notes that the Whitall Tatum Company of New Jersey used the WT within triangle marking only for the period 1935-1938. It appears the mold seam is on diagonal corners (picture 2) and may be faint on the neck but it's there...
Chris