You should only amend your return if there is a major mistake, like an incorrect filing status or incorrect income. Since the omitted $45 can fall under the term "de minimis"  rule, no amended return is necessary.  This rule describes something that's too small or insignificant to be of importance.  

In general, since the  the tax would be less than $50, no amended return is recommended under the de minimus rule.  However, you may still file the amended return is you want to.

I received a 1099-INT for $249.97 after I e-filed my Federal and Alabama State Taxes.  They have both already been accepted. Do I need to amend my taxes returns for this amount of interest income?

Yes, I would suggest amending both your Federal and state returns to add this interest income.

How do I go about amending a mistake on my taxes? How do I start?

I want to amend file

Since they have both already been accepted and I am getting a refund on them both, is it okay to wait until I get the refunds to do the amended returns? I would be doing the amended returns BEFORE the tax deadline of this April 15.

@mistyann2

You can certainly wait to file your amended returns. Actually, you should wait, in case you receive another income document.

If I wait, but do them both (Federal & AL State) before April 15, will there be fines since I received a refund? I don't think $250 extra income will make a lot of difference, but I'm just wondering about fines.

Also, does it cost money with Turbo Tax (this is how I e-filed both returns) to do an Amendment to my returns? I do know I will have to mail them both in.

No, you should not be assessed a penalty based on the information that you presented.  You will not have to pay money to TurboTax for your amended return, unless you need to upgrade to a higher version to add something.  For example, you are adding a business when you only had W2 income on your original return.

You can  amend your return in TurboTax after your return has been processed (generally 10-21 days) and you have received your refund, if any.    

TurboTax expects the Form 1040X, Amended U.S. Individual Income Tax Return to be available for customers to amend their returns on February 5, 2020.

You should not try to amend your return until it has been fully processed and you have received your refund or your payment has cleared.

Amended returns do not “catch up” to your original return and replace them;  they are processed as two separate returns.  

Amended returns have to be printed and filed by mail.  It can take the IRS up to 12 weeks or longer to process them.  

If you are due a larger refund than on your original return, your amended return should only show the difference and you will receive a separate check for it.  If you owe money on your amended return, it will show only the new amount owed, you will have to mail a check with the return.