I converted part of my DAI to xDAI, but that does not show up in my wallet.

The first thing to check is whether you have enabled xDai Network.

Click Settings, then Select Active Networks, then enable xDai network. Go back to Wallet tab you should be able to see xDai token card with the right balance.

xDai is not a token issued through a smart contract, xDai is the native cryptocurrency on xDai network. Like ETH on Ethereum network.