Sounds like you had an A/C compressor catastrophic failure–aka “black death” as noted above.
Flushing out components (like the condenser and evaporator core) is not reliable, as the design of a/c systems over the last 10 years or so has resuled in condensers with flow tubes so small and convoluted that flushing out all the debris is impossible. You may choose to have a shop try to flush the system, but no knowledgeable upright shop would give you any warranty on the compressor–so that’s an expensive gamble.
Find a good independent shop, they should be able to replace the a/c components as needed for under 2 grand. That’s a lot better than 3400.