Board Game Arena

I seemed to have shot myself in the foot with no way to recover.

After "Getting" 2 separate tiles, i have a found myself stuck with 10 + extra tiles.
Is it not possible to lower your current sets with new numbers?
If i have a run of 2-3-4, can i not get a 1 to lower the run's value?

That's correct, all public sets created with "Get" action are fixed in place, so in this case you'd be unable to win the round.