Hi there and
to the forums!
Therm has given the very best advice and I do hope you're able to get your poor guy into an avian vet right away
His foot certainly does not look well.
Also, I'm glad to hear you're not letting your sister care for your budgie anymore--I'm very surprised (and relieved!) he got through the cat attack without medical attention, as cats carry harmful bacteria that can make budgies very sick, or even be fatal, even without biting them or causing for them to bleed!
I hope your little boy can find a cure to his foot, please keep us posted!
You might try giving him some room temperature, unsweetened chamomile tea as it is a relaxant and may help him with the pain. If he'll stand in a shallow pan of it, that may help to, but don't force him. If he drinks it, that's great.
In the meantime, be sure to read through the budgie articles and "stickies" (posts stuck to the top of each subforum for easy reference) to ensure you're up to date on the best budgie care and practices
Best of luck!