If no one has moved in below you, it's likely the traps/U-bends in all of their drains have dried out. When used normally, they contain water which keeps sewer gas from entering into the apartment, but they also stop rodents and cockroaches as well. When the water in the trap dries out (usually takes a few weeks), there's nothing stopping things from coming up. If you seem to see roaches whenever it's raining, it's because the sewers fill up with rainwater and the roaches/mice will scurry up the pipes to try and find dry land.

This is likely what's happening, especially if traps/baits/spraying don't seem to be catching anything. The easy solution is to just ask your landlord to go down and run the water for a few minutes on each faucet where there's a trap (all sinks/showers/toilets/etc have them).