ICO coins are usually ERC20, you must receive them with a wallet that supports ERC20, and there must be transaction record in block explorer.
All ERC20 transactions can be checked here:
https://etherscan.io/ .You just need to enter your receiving address and click on "GO".
If the coins your bought are not ERC20, you can also check your transaction through the block explorer, usually you can find it on the official website of coin.
If your coin have no any proof of the transactions in explorer, then your bought may be other electronic currencies that are not part of crypto, or have a problem with your wallet,and another worst possibility is that you have been cheated.