Recharacterizing is definitely the way to go, but in fairness you would have received some tax benefit, just not as much as recharacterizing to Roth would give you. (If you aren't interested in the details, no need to read below).

A nondeductible Traditional IRA still grows tax-free while inside the IRA. This is not true for taxable accounts. In other words, every single time you sell inside a taxable account, you'll have to pay some tax on the gains--you don't have to do that for any kind of IRA, even if the contribution was nondeductible.

Second, the nondeductible contribution is still only taxed once. When you start withdrawing from a Traditional IRA and you have nondeductible contributions, those nondeductible contributions come back out tax free. For example, suppose you had $1,000 of nondeductible contributions and a total account balance of $100,000. This means that 1% of your account balance was nondeductible and had already been taxed. Therefore, for every $100 you withdraw from the account, only $99 is taxable. 1% of your withdrawal--equivalent to the 1% of the account that was nondeductible in the first place--is not taxed when withdrawing later.