Quick answer: On a Switch, open the Nintendo eShop and select your account — your balance shows at the top of the screen. You can also see it by signing in to your Nintendo Account in any web browser.
Checking your eShop balance takes only a few seconds, and it's the first thing to do if you ever think a code didn't go through. Here are both ways to see it.
You don't even need your console. Sign in to your Nintendo Account in a browser and your eShop balance is shown in your account's shop area. Just make sure you're signing in with the same account you redeemed your card on.
If the balance is lower than you think it should be, you may be checking a different profile than the one you redeemed on — see eShop funds not showing up. And remember a Switch Online membership card adds time, not a dollar balance.