I've noticed that the counter for when I can vote seems to reset when I log in from a different computer. I travel between two cities a lot (home and school), so this is bound to happen a lot. I don't want to be vote-abusing, but it also gets annoying when the "You're able to vote for NX." notification keeps appearing in my chats. Is it alright if I just take the vote? Or is there a way to cancel it?
No it's not alright to vote more than once per day. I don't have a solution to your problem though, far as I know it shouldn't display that message if you play using the account you voted on.
I have three accounts, and I vote on the alts sometimes instead of the main. (For getting pets, or if I'm too lazy to log out while pqing and don't want to miss a vote.) I haven't used others' accounts nor lent out mine. This glitch happened to me twice: once on the 8th, when taking my laptop to my relatives' home, and once on Monday, after returning to my desktop at my dorm from home. I don't know if switching IP addresses had anything to do with it, but it seems odd, since all three IP addresses (relatives' home, my home, my dorm) are all within 2 hours drive of each other.
What you can try is to log into the account you already voted on whenever you get that message and then log out and back into a different account, might work.