Correct. The dollar value shown on wallet page is sum of all your coins converted to USD value at market price.
Is there a possibility in bittrex to see your initial exchange rate in usd? And are there any other exchanges where you can buy with Euros?
You can check you history ofy our trades on the orders page. FYI: Bittrex does not support any fiat trades. Only USDT.
If you want to trade with euro you can try bitstamp, cex, coinbase, kraken...