So i did all the 36 challenges for the skins. I later deleted my monk, and have started leveling one again. when i reached 111, i couldnt xmog the mage tower skins.
Didnt they state that the skins would be unlocked account wide?
If not, i am totally screwed 
I was under the impression once you unlocked them theyâd be available account wide but not the unlocking. Iâll have to do some digging.
Unlocking Tints
After unlocking the base style through the Challenge, you can unlock other artifact tints by defeating heroic KilâJaeden, winning 10 rated battlegrounds, and and defeating all Legion bosses. Youâll also be awarded the achievement
A Challenging Look.
In Patch 7.3, you do not need to have the Challenge Appearance equipped to earn credit towards the tints. You simply have to complete the activities on the character you earned the initial tint onâyou donât even need the same spec or artifact equipped.
Would seem to indicate you have to complete the requirements on the character you unlocked it on.
Just restore your old monk.
Restore your old monk and ensure you have completed the full quest that gives you there [A Challenging Look] achievement on that character. Honestly, I have been using my Tower Transmogs on a number of characters to only find out I hadnât turned in the final quest on the original character!
Go check in with Khadgar (Or was it Kalec?) in Legion Dalaran on your restored Monk.
I cant restore my old monk, it shares a name with a active toon now
You can still restore it, but you will have to rename it.
This!!
It will just flag up for a free rename.
It gives me an error when i try to, something about sharing a name with a active toon.
File a ticket. My friend had the same issue. He had to get a GM to do the undelete.
Hmm, but i shouldnt have to?.. Pretty sure Ion said that it would be account unlocked. Wish i could find the transcript 
Sadly i spend a few gold on my new monk with flying etc haha, tho i would gladly give that up if i cant get my mage tower skins back otherwise!
EDIT: found this.
Artifact appearances, including completed Mage Tower challenge appearances, are account wide. You can transmogrify a non-artifact weapon with an artifact appearance unlocked by a different character on the account. The character must be the appropriate class and specialization for the Artifact, and all of the other standard transmogrification restrictions must be met.
That confirms that the unlocked appearances are account wide, not that you can unlock further recolours on a character that doesnât have them
Start a ticket to get help to undelete your original monk.
Transmogs from quests usually tie in to the characters. So deleting the monk made the account have no characters with completion to share.
I lost Anathema because a server merge caused my old priest to be innactive, but as soon as I did the forced rename I got it again. (and I now have an achievement date which is literally impossible since the quest doesnât exist anymore)
also found this: on mmo from a q&a transcript
" * Artifact appearances earned today will be account wide, you will be able to use them on a new alt of the same class."
I didnt mention color variants.
Are monks limited to one per realm? That could be the issue if you have a new one.
Tested that theory and no you can have many monks on one realm.
That means if you have unlocked the appearance you can use it on any monk on your account.
Not that you can unlock further appearances on a monk that doesnât have it.
You cant transmog the Artifact itself apparently. My Alliance DH had the same issue but could transmog other weapons into the MT Artifact Tints i unlocked with my Horde DH once i replaced the Artifact.
Artifact appearances for transmog are account wide but you have to log on the character that has unlocked it after 8.0. The system scans your unlocked artifact appearances on that particular character the moment you log in and adds the ones that arenât in your collection yet. So if you deleted your monk before 8.0 you have to restore it.
This is also why you have to relog after unlocking new artifact appearnce to be able to use it as a transmog.
Tried that 
seeing that the artifacts now are âusedâ⌠Sadly i only get the generic options, aka default skins.
This could be the issue, nice input! i am so screwed
Does it actively prevent you? Would it not prompt a name change? Try it! Even deleting the other toon for 14 days (since restoring the monk puts you on a restore cooldown) is worth making sure you donât lose the appearances thatâll never be available again!
14 Days > Forever