Do you have any suggestions for over-the-counter probiotics? And in your opinion, what dosage would be appropriate?

I recommend starting with Probaclac probiotics. They have a good quality-to-price ratio and can help with reducing diarrhea. Take 1 capsule twice a day regularly. If you don't see any improvement after 15 days, you could try Bio-K, which is more expensive but contains effective lactobacilli.