Yes, that sounds like the correct conclusion. Sticky caliper. As a result you seem to have boiled your fluid giving you the spongy pedal, otherwise you'd still be able to brake, but with a strong pull to the passenger side.
Rebuild the caliper and change the fluid. The pads are likely glazed up and the disc potentially warped. The glazing will wear off but the disc might need replacement.
One thing I do wonder though is which light came on. Hot brakes should not trip the wear indicator.
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