I got sick

It may be helpful to know that the chemical name of the active ingredient in Immodium is loperamide.

I do not know whether that is available without a prescription in the Netherlands. The internet tells me that non-prescription drugs can be bought at a drogist, but for prescription meds one must go to an apotheke.

Be sure to keep up your fluid intake if the problem persists. And consider electrolyte replacement if you're still unwell, say, tomorrow. I do NOT have a medical background, but I've been through a bacterial infection that lasted 5 days, and even though I thought I was drinking enough fluids, I still ended up dehydrated and low in potassium. The pharmacist in Slovenia was able to sell me a powder to be mixed with water, once she understood what I needed. Linguistically, that one was a bit tricky. I would think it would be easier in the Netherlands.

Any pharmacy or drugstore sells itover the counter, without prescription, including the Etos and Kruidvat chains.

Are you staying in a hotel? Ask the front desk to direct you to the nearest pharmacy.

Go to the nearest pharmacy, they will be able to help you. Grocery stores etc do not carry those kind of meds.

"Grocery stores etc do not carry those kind of meds."

Actually, they do:
https://www.ah.nl/producten/product/wi362933/ah-diarreeremmer-loperamide-hcl
https://www.spar.nl/imodium-diarree-remmer-capsules-1945602/
https://www.plus.nl/product/htp-huismerk-diarreeremmers-2mg-doos-10-stuks-407873
https://www.jumbo.com/jumbo-diarreeremmer-loperamide-hcl-2-mg-capsules-10-stuks/125707STK/

"The internet tells me that non-prescription drugs can be bought at a drogist, but for prescription meds one must go to an apotheke."
Almost correct. Non-prescription drugs can be bought in supermarkets, drogist (drug store) or apotheek (pharmacy). Prescription drugs can only be bought at an apotheek. Usually this can only be done after a doctor/physician in NL issued a prescription.