If it isn't confirmed yet, then the merchant or service probably won't update your account. You'll need to wait for the transaction to receive a few confirmations.
Would you be willing to share the transaction ID or the address and amount so that we could take a look at the transaction and give you a better understanding of what is going on?
Some desktop wallets to consider are:
Desktop:
- Bitcoin Core
- MultiBit
- Armory
- Electrum
There are also mobile wallets for Android or iOS, and there are some hardware wallets as well.
Have you used the android/IOS wallets? Are they safe? Is there a bitcoin core for mobile?
Due to the size and CPU constraints, Bitcoin Core for mobile is not possible. SPV wallets are mostly created for android.
Keep in mind I would only keep spending money on a mobile. It just is to accessible and possible for bad things to happen.
I highly suggest looking into cold storage. There are multiple options, or if afraid of that look into hardware wallet.
Did your BTC show up on other website?