...with an empty hand...As far as a water hole be careful not to right click it... will cause dehydration.
Snip...
I had this issue when I setup my obsidian barrel. Most times it worked no issues but sometimes I would get dehydration buff and barrel would stop filling/converting. Then I realized the only common factor [when it didn't work] was using an empty hotbar slot. Make sure something is in your hand/hotbar slot when clicking through placed water.
You can make it from the ship [with no trench/wall protection] to the city and get a trench/wall setup [and some kinda shelter within the enclosure] all in one day [I'm assuming day 2]? If so, better player than me....Snip
Setup a perimeter by digging a trench and building a wall (if you don't try to make it too large you should be fine). The city will provide all the water and food you need early on if you progress at a reasonable rate and the cobwebs you thought were useless in other runs can get you a very early bed.
Don't you need a sword to turn cobwebs into string? Which means smeltry [and lava] or finding sword-blade drop?