Usually when UI stops working it's due to an addon interfering. You can do some troubleshooting by unchecking all your addons before logging in, if transmog works you know it was one of your addons. You can then go through and add them back one at a time.
Personally I might just go and make sure everything is up to date first. If you have some wildly outdated addons that seem to have been dropped by the creator (no updates within the last couple patches), it may be best to seek out alternatives.
Otherwise you can do a full interface reset