You're not going to like what you're about to find out about cockroaches. As a native New Yorker I am, like all New Yorkers, a de facto cockroach expert.
If you live in a 10 unit building then there are 10+ ways that things can go horribly wrong every day. Someone moves in. Their last place had roaches. BOOM! The new place has roaches. And roaches are quite expeditious at colonizing new territory (your apartment).
Roaches can eat anything. As you go about your apartment bits of skin, food, assorted detritus and the flotsam and jetsam generated by being a biological entity are all food to a roach. Grease in your pipe? Delish! Earwax? Yum! If you really want to freak the fuck out youtube "roach in ear".
That's the bad news. The good news is you don't seem to have much of an infestation using some chemical controls is fully warranted, safe, reasonable and effective.
do you own or rent? If you rent call the landlord/property manager asap and quietly lose your shit over the infestation. Exagerate for effect. just a bit. Don't over do it. Most prop managers that give a rats ass about thier newly remodeled buildings prefer pain in the ass but fastidious tenants like yourself over destructive, sloppy ones. So long as you're up on the rent.
And document, document, document. Take a pic or the roaches and write a letter and send it registered mail or email it requesting a return receipt. Keep records. Buy sa roach motel and keep the receipt, etc. If the roach problem continues and you documented the problems you may find it much easier to get out the lease or withhold rent.
Good luck.