I made a bitcoin transaction from btc core to bittrex with quite low fee, yet looks like it went through in 4-5 days, now I have it "sent" for 2 days but I still can't see it in my bittrex balance... is this anything to worry about or is the network this goddamn busy or something?
If it went through, AKA "Confirmed", then there is indeed a problem, and you shouldn't necessary worry, but definitely look into the issue and contact bitrrex's support, as they probably somehow haven't credited your deposit.
I believe that either after 1 or 6 confirmations Bittrex should show your deposited BTC in your account, but don't quote me on that.
Do you have a transaction ID so i can take a look?