There are lots of different strains of cat flu in the same way there are different strains of human flu. Some serious (and thankfully rare) ones can involve mouth ulcers and you will always see a good vet inspect the mouth to make sure when examining a cat flu suspect. The more serious strains can be really quite horrific and the mortality rate is high.
The more usual milder strains can show as runny/sticky eyes and or sneezing fits and are very easily treated with the correct antibiotic and cleaning regime. I feel certain your new cat has a mild strain as a kitten carrying a serious strain is often unlikely to survive.
It does not always follow that a cat that has had flu becomes a carrier, however when they are carriers they can 'shed' the virus again and have little flare ups which require treatment to manage such as in Oscar's case.
In all cases you should still vaccinate a flu carrier against cat flu as they will be protected from other more serious strains.
