I am looking for my IMEI number for a phone I bought through Apple

See here:

Find the serial number or IMEI on your iPhone, iPad, or iPod touch - Apple Support

You may also be able to get the information by logging into your account with your cellular provider or by contacting your cellular provider's customer service folks.

1.) Settings

2.) General

3.) About

**You will see a list of things, look until you see IMEI a long with the IMEI information with it.**

4.) IMEI

1.) Settings

2.) General

3.) About

You will see a list of things, look until you see

4.) IMEI

OP says the phone is locked so he cannot go to Settings.