If you have sweeped the funds already then the bitcoins are in your electrum wallet already, just go to History tab, you'll see your transaction there, right click on it and click view on block explorer, that will show you how much fee was added and based on that you can estimate how long will it take for your Tx to get confirmed.
Also, make sure to keep backup of your Seed.
You could pass your TXID over to us, we can help you estimate the TX time. I would recommend storing your bitcoin in electrum for as little time as possible, and put your coins back onto core. Core is safer, and you've already said you have a relatively large sum of coins?
Id say electrum is fine, esp. if you cant get core to sync (like OP). To follow up on your question about the TX ID, maybe @Samorr you can post the address you initially received the coins on. This would allow us to follow the transaction trail and give you an estimate when the TX should confirm. Given the time that passed, it might already be confirmed though.