No! Your iPhone cannot be accessed remotely. Your iCloud account can be accessed remotely and changes to that would be reflected on your device. Some people confuse that by thinking it is their device that is being accessed and that is not true.
For example, when using iCloud Photos, a person that has access to your iCloud account can delete and add pictures to iCloud, and those changes will be reflected on your device when the data has synced. It certainly is NOT your device that is being accessed remotely making those changes.
For access to your iCloud account, you are going to need the email address associated with it. You can reset the password without the phone number using Account Recovery, but you will still need to know the email address.
Apple can only offer tips to help you find your Apple Account email, but honestly it is not useful if you do not have another device using that account.
If you forgot your Apple Account primary email address or phone number - Apple Support
Without that information, you have been given the correct recommendation to create a new Apple Account.