The problem is that when you sync iPhone with google contacts through Microsoft Exchange all numbers with custom labels just don't sync to iPhone. So is there any solution to this problem?
Depends on how you sync Google Contacts to iPhone. If you do it by setting up the gmail account on your iPhone using the Exchange option, then fields in your Google contacts do not transfer to the phone. But the advantage of using the Exchange way is that syncing is instant--edit a contact on the phone and it changes in your Google account as well. If you sync the contacts using the gmail option, the custom fields in Google contacts DO show up on your phone. The disadvantage is that syncing only happens when you sync the phone with iTunes on your computer. That's my experience, anyway. I would like to know how to have both: sync custom field labels and sync instantly on the fly with every edit.
Try the following:
Export all your Gmail contacts in the form of a vCard file.
Once you have the vCard file saved to your PC, import it to your iPhone with the help of the following tool:
If by custom labels you mean contact groups, then you can also recreate the contact groups on your iPhone again via using the above program.
I found a great solution and I've used it myself.
You should turn off your exchange contacts-sync first (confirm it will remove your contacts) and then you should follow the directions on this support page of Google.