You're right in that indexing will do nothing to improve the insert performance (if anything it might hurt it due to extra overhead).
If inserts are slow it could be due to external factors such as the IO performance of the hardware running your SQL Server instance or it could be contention at the database or table level due to other queries. You'll need to get the performance profiler running to determine the cause.
If you're performing the inserts sequentially, you may want to look into performing a bulk insert operation instead which will have better performance characteristics.
And finally, some food for thought, if you're doing 10K inserts every 5 seconds you might want to consider a NoSQL database for bulk storage since they tend to have better performance characteristics for this type of application where you have large and frequent writes.