What is the address that you have sent the Bitcoins from CoinURL to? Is your Bitcoin Core fully synchronized (a tick at bottom right).
It says "Synchronizing with network: 2years and 19weeks behind"
The transaction will only appear when Bitcoin Core has a tick at the bottom right or when Bitcoin Core has synchronized to a block that the transaction was mined in or when Bitcoin Core synchronizes to a block that is close to the time when the TX appeared if it's unconfirmed.
So it's going to take 2years for it to syncronize for me? I'm new to using Core, thought it would be more secure and better then a webased one
It depends on a few factors, your internet connection speed, disk I/O and CPU speed. With the headers-first synchronization, it is much faster since blocks are downloaded simultaneously, like torrent. CPU speed is the most likely bottleneck here, client have to verify each block individually to ensure that it is valid. Core is definitely more secure than webwallets and most other wallet in terms of its trust towards a third party. Core does not trust anyone. However, other SPV clients like Multibit and Electrum, although trusts the miner fully, have more advanced features like Hierarchical deterministic seeds and users would only have to back it up once compared to core which requires a backup every 100 transactions. It does trust the miners to enforce the network rules though.
IMO, Electrum is trusted enough. I would recommend you to wait for Bitcoin Core to synchronize first and ensure that you have ~60GB of disk space. Could you give us the address so we can ensure that the coins have indeed been sent to your address?
If you absolutely absolutely need your coins fast, I have written a short answer here to export the private key:
https://bitcointalk.org/index.php?topic=1276902.msg13158003#msg13158003.