First, check if you have water ingress into the boot (trunk if in
USA!).
Check the behind any lining at the back of the wheel arches for pools
of water - sunroof drain popped out of hole, electric aerial drain
popped out of hole, other leak (can need a hose to find it).

Second, realise you can not solve this except by serious application
of new metal, but you can slow it down to something which is
controlled for about 3-4-5yrs depending on how severe it is. Some cars
do however have a problem in the wheel arch area - a weld in the wrong
place can let moisture in to a seam, a seam may have the
weatherproofing which has failed.

The best way to remove rust without removing metal is to use a 3M
Clean n Strip disc.
These come in black or purple (XT), the latter is simply a faster
version. You can get a version which fits into a cordless drill, or
into an angle grinder. To be honest they are so fast and powerful that
an angle grinder is quite unnecessary - even a sub 12V cordless drill
with a Clean-n-Strip disc will cut through paint, primer/galvanising,
rust and clean it to a surprisingly bright finish and get into the
pores. It will not get deep into the "worm hole pores", but it will
shift the mill-scale leaving pitting.

Then you really want something electrochemical to prevent rust - sadly
most cars do not have galvanised wheel arches, those that do tend to
have very limited micron depth which erodes pretty easily. The problem
is, the more zinc in the treatment a) the more expensive b) the
heavier the can c) the more difficult to get cellulose paint to stick
to it! So generally go for the highest zinc content paint you can, you
then need a primer on top which permits car spray paint to stick to it
(galvanising metal primer). Car trailer people use Zinga or
Galvafroid, but that needs an alkyd paint (IIRC) on top or a
galvanising metal primer which is typically applied with a brush.
Pretty it is not, but it is very effective at slowing down corrosion
even from the other side (as it should be, I think 250ml of Galvafroid
is about £20 these days and weighs like a lump of lead likewise).

The best solution would be a 2pk zinc loaded epoxy mastic, but they
are expensive. Colleague used it on a known atrocious for rust Merc
estate which was hammered (literally) as a "wheelbarrow" in place of a
van, because he wanted a decent automatic. It worked very well, but
was very expensive - or would have been, he actually handles
industrial coatings and thus it was little more than a sample to his
supplier.

Wire brush is a lot of noise and slow, 3M clean-n-strip is very quick
and extremely effective.
There is a "Roloc" version which has a small reverse-thread "stick" in
the middle rather than a proper shaft/spindle, it requires a "Roloc"
adapter which adds to the cost. A cordless drill is plenty powerful
(you are not stripping an entire car).

Rust is a worm, it travels as dark patches under paint - but with a
good very high content zinc primer you can actually slow it down. You
can not stop it, but it is nice to strip a bit off you did 1-2yrs ago
and find the progression is minimal, then 4yrs later you find the
really bad bit has travelled a bit bigger - but 4yrs is a long time.
Some cars are notorious which requires fresh metal and that requires
careful practice with a MIG because car sheet metal is very thin (you
tack it and let the metal cool since you are fighting erosion).

Frost Automotive do various solutions (they carry the 3M Clean n
Strip, but I can not remember which is the cordless drill "pad on a
spindle fit-n-go" part number). They do various primers. POR-15 is a
favourite anti-rust, but you can not weld metal after using it and
frankly since you can only put it on one side of the steel which is
rusting from the other side it seems pointless. You need an
electrochemical solution from experience and comparing just about
everything on the market.