The PCB looks nice. It's not essential for this case but everyone has switched from 90º corners to 45º corners because it causes problems in high frequency circuits.
Wow that SCH is a bit of a mess. If you look at some of the solid traces they have ratsnests bypassing them, and if you look at the components they have red pins so they aren't actually connected. One trick is to make sure all the connections are green, and that if you move parts around the traces stay connected. Like you could have a 4 wire junction where trace 1 is connected to 2, and a 2nd junction sitting on top where 3 is connected to 4. All pins will show green, but 1,2 isn't connected to 3,4.
The usual way is do the SCH first, and make sure everything is actually connected. Then go into PCB and click on the pin you want to run a trace from, and every place where it can connect to will turn yellow. Then run a solid track between the 2 points you picked and that ratsnest should disappear.
If you are happy with the PCB, you might be able to go to SCH/routing/select all traces/delete, and just redo the traces knowing what you know now. Try it on a copy so you can compare it to the orig.