Can I get back the money I was penalized for not having health insurance for 2018

No. The government action that reduced the penalty for failing to have adequate insurance to zero did so for tax year 2019 and going forward.

 

There is no provision to get refunds for penalties incurred in tax year 2018 and before.

What if I get an exempt

If you were to get an exemption for 2018, you could file an amended return. 

 

You can find out more about exemptions here. 

 

For TurboTax Online, simply login to your account and select 2018. Then click on Amend (change) a return. If you used our CD/download product, sign back into your return and select “Amend a filed return.

 

You can find out more about amending a return here.