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Or alternatively, your mattress may be too hard. I've gotten a stiff back after spending the night on a harder-than-I'm-used-to mattress before (or on the floor/ground). So, if laying on the floor doesn't help, it might be that. In any case, splurge and buy a decent mattress as soon as you can afford it, and once you've figured out what firmness you need.

Two things you should never be afraid to spend good money on: a quality mattress, and quality shoes. Both will save you from sore muscles.