Can I sue a store for a slip and fall accident if I didn't seek medical assistance?

Sure, but it would be silly to do that. No lawyer with any competence would take the case, because it isn't worth more than pocket change.

Michigan law imposes restrictions on slip and fall lawsuits in that you cannot have a successful claim if the condition which caused the fall was "open & obvious" such that you should have been able to appreciate the hazard and have avoided it. There are a few exceptions to that law, and some circumstances are not open & obvious, so the specific facts of your situation would have to be explored to determine if there was a viable claim. However, even if the claim is viable, you must have suffered damages in order for compensation to be considered. So a fall without injury, or without treatment that would show the nature and extent of the injury, would be unlikely to allow a case, or any case would perhaps be considered marginal. Again, the specific facts as to any injury would need to be explored. In other words, your recitation of the situation doesn't really allow one to determine whether they may, or may not, be a viable case.