No, they are not obligated to give you their insurance information. If you believe they were at fault but will not voluntarily compensate you (and their insurer will also not voluntarily compensate you), you can sue the restaurant (you sue the restaurant, not the insurer) for your out-of-pocket (not paid by your health insurance or Medicare/Caid) medical bills; lost wages, if any; reduced earning potential, if provably in the future, you cannot earn or work as much; and for long lasting and signficant disability or life impairment (lasting many weeks at a minimum), some amount for "pain and suffering." (Note that the amount you can get for pain and suffering is related to the severity of the disability and duration, with minor to moderate disability or impairment only lasting a few weeks not being worth much at all.)
Note further that the restaurant is only liable if they were at fault. You write that the floor was uneven; minor unevenness will not make them at fault, since many buildings have floors that are not perfectly even. Only a floor which is unreasonably dangerous might make them liable.
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