Now that OP is back home, there is nothing to be done other than look at ways in which she might cut her losses. But, before doing that OP really needs to provide some accurate facts without emotion.

I presume that she did not purchase or otherwise carry travel insurance. But, it is possible that the CC she used for the tickets does carry some coverage and might possibly cover this particular situation (although pretty slim chance).

OP says that her train was 2-1/2 hours late. But, the facts posted above suggest that her train was only 1:12 late, e.g., less than 1/2 as late as she says. First, fibbing to an insurance company is a bad idea and second, it's significant here because if she was scheduled to arrive at CHI at 3:58, she would likely have missed her 5:55 flight anyway. In other words, while Amtrak's delay was frustrating, it likely was not the cause of her missed flight.

OP can also call Spirit and beg. She is not likely to get anywhere, especially with Spirit. But, if she does, she should be ready to give Spirit the new dates she wants on the spot. Do not say you will think about it and call back.

For the future:
1. Carry insurance
2. Make sure your phone is charged (but, remember airports and train stations are places which still have pay phones -- so not calling was a very big mistake).
3. If you are on separate tickets, e.g. Amtrak to Spirit or even two different airlines, allow plenty of time. Plenty of time means at least double the time that an experienced Chicago driver thinks it will take and adds in the time you need to make it through security and to your gate.