It's hard to picture what you are saying, but it sounds like you had to merge across several lanes of fast-moving busy traffic, some of which is actually merging onto the interstate, to get to a left turn lane that also allows for people to go straight when the light doesn't have an arrow? If I'm close, this sounds like a losing situation for a slow-moving bicycle.
How would a pedestrian handle this? Perhaps at this intersection when traffic is heavy, using the crosswalk might be easier to manage. There's no shame in this. It's better to live to ride another day. Perhaps you can make your left turn elsewhere as well. Either further ahead or earlier. I know that's not always possible, though.