Congratulations on your aunt's new family member! As a fellow lover of Siamese, let her know that she is in for a treat!!
How old is your cat and when did the veterinarian see her last? Where did she come from?
Runny noses and upper respiratory infections are not uncommon in cats, especially if she came from an environment with lots of other cats. Many of these infections are somewhat self-limiting, but it is always best to get her checked by the veterinarian.
Cats who don't groom are often not feeling well, so again, it sounds like a trip to your vet is in order. Ear infections could certainly cause the balance issues you describe.
Let us know how she is doing and maybe we can provide some more detailed answers for you.