Sorry to see Brigadoonery being propagated on RootsChat.
The surname Andrews is a patronymic, from the given name Andrew, which is popular in Scotland because it is the name of our patron saint. Other variants include Anderson.
However the given name occurs all over Europe, and consequently versions of the patronymic surname also occur all over Europe including England, Wales and Ireland, Greece, Russia and Scandinavia in particular.
It is undoubtedly true that there were families surnamed Andrews who came under Clan Ross, but to suggest that all people with the surname were connected to Clan Ross is misleading, as you have discovered.
If you can trace your ancestry by properly documented means to Clan Ross or any other of the clans, that is great. But you must not assume that your particular line has to be associated with any clan. The idea that every Scot must belong to a clan is quite erroneous.
The clans were a social feature of the Gaelic-speaking Highlands, not of the Lowlands where the majority of the population lived, though since Sir Walter Scott romanticised the Highlands and revived interest in clans and tartans in the early 19th century many Lowland and Border families have reinvented themselves as clans. Many a Lowlander in late mediaeval and early modern times would have been shocked and horrified at the suggestion that (s)he was connected to any clan.
As for tartan, there is no tartan police, and there are very few tartan setts (designs) that can be authenticated back much before the early 19th century. You could wear Anderson tartan, or you could be guided by the 'official register', or just find a tartan you like and get on with enjoying wearing it.