Query about missed flight due to delay at the counter to check baggage
 

Hi,
This is not a complaint. This morning I missed my flight due to the long que at the Detroit airport. Having arrived one hour fifty minutes before departure time, I got into the line to check my baggage in and after getting halfway the line one of the spirit staff member asked if I have a boarding pass which I did not, and asked me to goto the kiosk to get it and informed me that I could back in the line to my spot. I initially had trouble getting the boarding pass and it took me nearly 5-10 minutes. The boarding didn't have the seat number, I showed it to the staff member upon which she directed me to the agent assistance line where I spent the next 50 minutes. Finally after getting to the counter I was told I didn't have enough time to get to the gate and that it was too late to check my bag. I was also informed that there were no available flights till Saturday. By now, I was nervous and stared checking for another airlines to book a ticket and just left the airport dejected. I need to know anyone could tell me how to proceed forward and what are my rights in this situation.
I understand I've written quite the long query, I really appreciate your patience if you could go through this and guide me.
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