Yes, of course.
Why did you change hotels? You want another hotel to know about your little problem? If I've stayed at the hotel a few more nights, I come to the front desk and say: "I'm so sorry, I had a little problem last night and I need to change the sheets, is that possible? I will of course cover the higher costs".
I have never had a problem with this and they have never asked me for anything. In these cases I leave a larger tip than usual in the room.
If it's the last night I only leave a larger tip.
I had an unpleasant thing happen to me once. I had a nosebleed last night, not a little, but a lot, if you saw the bed in the morning you would have assumed someone had been killed there. It was the last day, but the damage was extensive, so I told the front desk that I had a nosebleed during the night and that the pillow and sheets were from it. I wanted them to come take a look at it and asked for baking soda or vinegar to clean up the damage (I have experience with this). The front desk told me that it was okay, that it would happen, and that they would take care of it. However, I was surprised when they later wrote that the damage was extensive and that a new set had to be bought for that room (4 beds) and the amount was really high. So I wrote to them saying that I could clean it and that I tried to arrange it at the reception, but they didn't even come to see me and that I definitely didn't agree with this and wouldn't pay them anything. With the understanding that if it was dealt with on the spot we would take pictures of it and that I am insured for these things so we could pass it on to the insurance company. I sent them the contact info for my insurance company and let them handle it with them. They never got back to me.
Rather, I recommend contacting the hotel before you arrive, or putting in a note: "For medical reasons, please. Would it be possible to install bed protection and a larger basket for incontinence items in the bathroom. Thank you very much."