First, if you under age 59-1/2, you will pay an extra 10% penalty for early withdrawal. Did you mean to do this?
Second, you have 60 days from making an IRA withdrawal to change your mind and put the money back. If the rest of this information makes you re-think your decision and it is less than 60 days, you can return the money to have more time to think about what you need to do.
Now, it sounds like you already had an IRA. Assuming that to be true, you now have a non-deductible (already taxed) basis in your IRA. This is recorded on your form 8606. You need to keep copies of your form 8606 basically for the rest of your life. (Technically you only need the most recent one, but if you keep all of them you can prove the chain of events.)
Suppose your IRA is worth $50,000 but it contains $7000 of non-deductible contributions. And suppose you withdraw $5000. Because 14% of your IRA is non-deductible basis, 14% of the withdrawal ($700) is tax-free and the remaining $4300 is taxable. Then, since you withdrew $700 of the non-deductible basis, your remaining IRA with a balance of $45,000 has a non-deductible basis of $6,300. (All your withdrawals for 2022 are combined on your 2022 and your non-taxable percentage determined using the balance at the end of the year.)
Also note that all your traditional IRA balances are aggregated (combined) for this purpose. If you have an IRA at Smith bank that is all deductible, and another IRA at Jones bank that has some non-deductible contributions, all your balances are added together and any withdrawal from either bank will be partly taxable and partly non-taxable.
Then in 2023, if you make another withdrawal, the non-taxable portion of the withdrawal will be calculated using the 2023 balance of the IRA and the updated non-deductible basis, and so on until you empty the account.
You can't "get it back." You are stuck having a non-deductible basis in your IRA forever, unless you withdraw and close all your traditional IRAs or convert them to a Roth IRA. In the example above with a $50,000 IRA with a $7000 non-deductible basis, if you converted the entire IRA to a Roth IRA, $7000 would be tax-free and you would pay income tax on the other $43,000. But then, since it's a Roth IRA, you would never pay income tax again on any withdrawal.
