Further to my earlier reply, the "Didn't get the code?" link should also be present when the app presents you with a screen to enter your OTP. Following the link should allow you to request the OTP to be sent to your registered email:
You're not the only one. Public Mobile's system is glitchy. Many customers are not receiving verification codes to their emails/phone number, and they cannot log into their accounts. I recommend you request cancellation. Staying customer with this horrendous company is simply not worth it.
Not sure about the app, but on web there's a link below the OTP entry box, to the effect "I didn't receive the code", which you can click to take you to a screen where you can choose to have the code sent to your registered email.