Can I change my gamertag without $10 fee?

Nope

Support cant even give free changes

Without a doubt that gamertag would be flagged as offensive, You won't be able to get it back and to change your current assigned gamertag you would need to pay $10, Theres no way around the gamertag change fee after a forced gamertag change.

i agree with everyone here the gamertag change fee applies this time as you have already changed your gamertag to a personalised one this maybe when your wife has created the account and might have changed the gamertag for free without noticing so the fee
of 10 USD OR 10EUROS 6.79GBP applies .

thanks everyone for the support you have given to this post aswell .

Hello!

Thank you for your post .I understand you are experiencing an issue with you with a recent gamertag change. If you selected a gamertag but accidentally accepted the changes without verifying your change, you must pay the gamertag change fee to correct it.
Unfortunately, there is no way to edit a gamertag without paying for a change.

It doesn't say anything about a forced Gamertag change and it says I've already used my free change? Is there a way I can see my Gamertag change history?

However, if they didnt change it do anyone else have access to your account? Also, more than likely, you going have to pay that $10 fee for a gamertag name change.