Based on my experience trying to build coilguns. So what I believe your saying.
1 you built a few coils yourself with some 22 gauge wire.
2 Your firing something down a 1/4 in tube for your barrel (what are you gonna use for projectiles?)
3, You've got your capacitor bank built out of disposable cameras, as well as the charge circuit.
Ok so what your planning on doing is making the arduino trigger the relays on in series to accelerate the projectile more efficiently.
That means turning on the first relay, then as the projectile passes shutting it off, and turning on the next. ANd having an individual capacitor bank for each coil.
Its not surprising you broke your multimeter, caps they have in disposable cameras can store more then enough power to hospitalize someone. Odds are, your relays wont trigger fast enough to get the series right (unless you lengthened the barrel, but then theres more friction). And with that much power as your first coil project, theres a very high chance your gonna hurt yourself. You say 22 AWG wire. How much voltage can the insulation take though?
Try something simple. 1 Coil, 1 cap/charger, and 1 relay (get something with high voltage and current ratings). Get that to work off your arduino (jsut have like a fire button on the arduino) Then move up to adding more coils and caps.
To note, its a lot easier to have a pair of coils on top of eachother each getting less power then it is to have 1 coil with 2x the power in it. And its safer. Now go experiment. I don't wanna see a news report of some guy hospitalizing himself with a homebrew coilgun though.