You need to get an x-ray and whatever supportive device needed at a hospital. You are wasting your time with home remedies and the splints sold in pharmacies. Personal experience on vacation, twice. When we are in a much saved-for, anticipated, planned, once-in-a-lifetime visit to a certain place, we deny anything and say say it's nothing, when what we really need is to be sure there's no break, get a proper walking device and proper care. I say this from accidents on two different trips where I tried wishing it away.
When I fell in a hole behind an alter in Brittany I refused to go to the hospital, kept saying it was nothing, tried wishing it away but in fact hobbed in pain on borrowed crutches and hopping on one foot. A week later in the US, the doctor x-rayed it. It was broken and he put me in a walking boot. My only compensation for such idiocy was the tech who said "Oh you're strong, one week on a broken foot." I should have listened to my friends who suggested we go to the local hospital to get it checked.
Another poster here, a friend, fell in a perched village ruin in France but kept trying to negotiate to herself that it was okay. A week later, swollen and blue, she ended up with surgery and a hospital stay.
So go get it checked out. Even if it's "just" a sprain, they might put you in a walking boot, which would really help stabilize you and allow you to walk on smooth surfaces--no climbing over rocks. You can get two hiking poles, which will help you to continue on. By the way, a foot sprain I did five years ago, which was immediately x-rayed, is still bothersome today and was a lot more painful than the break in the same foot. Wearing the walking boot for the sprain really helped.