To log in to your Instagram account, you need to enter both your username or email, and your password. Unfortunately, you can't log in to your account if you forget the username and email. However, Instagram enables you to recover the username through the Forgot Password form. Even though the form was created to help you recover your password, the email sent by Instagram also contains your username.
Recovering the Instagram Username
You can log in to Instagram using your username and password, so using the email address is not mandatory. However, you can find the email address by using the Forgot Password form. Tap "Forgot Password" on the login screen on your device and then tap "Username or Email" and type your username. Tap "Send a Password Reset Email" to have Instagram send you an email. Browse through your email accounts until you find the email from Instagram. Click or tap the link in the email to reset the password and then use the email account and new password to log in to your account.