Turned on a/c, and it didn't work. Now engine light is flashing, and car shakes alittle

I think it could have created an extra load on the engine, which exposed some pre-existing issues. A flashing engine light indicates presence of an engine misfire in progress. Diagnostic testing, including retrieving diagnostic trouble codes from the engine processor, is needed to determine where to focus attention on to troubleshoot the concern. Certainly, the air conditioning system is a concern, but first -- focus on the engine and engine performance issue and resolve that as without doing that you can cause further issues and damage elsewhere.