My DD is younger than yours so I can’t speak from experience in terms of a transition from two to one naps. Having said that, I have learnt that my DD needs a very specific amount of daytime sleep and if she gets too much we have long wakes in the middle of the night (of course, too little and she’s much more restless and likely to wake early for the day - you really can’t win!). For now, she is sleeping through. The only times she hasn’t slept through recently is when she’s slept over 2 hours in the daytime, and then she’s up at least an hour in the night, so it’s really stark.
When she started transitioning from three to two naps her sleep was awful and she was awake for 2 hours in the middle of the night every. single. night. I didn’t realise at first that the naps were the issue, as I could still manage to get her down for the third nap, even though she was fighting it and it was getting later and later, and she was exhausted by bedtime, still. But even though she went to sleep okay, she couldn’t get back to sleep quickly after she woke as she wasn’t tired enough. Her sleep didn’t automatically improve once she’d dropped the nap, either, but it did begin to get better and we got back to one or two quick wake ups. Have you noticed your DD’s sleep is better, or even different, on the days she’s having one nap at nursery? Given that she’s 15 months she probably is ready to drop the second nap - I would definitely give that a try, and stick with it for a couple of weeks as she may take a while to adjust. Sometimes with DD it felt like she needed 2.5 naps, and they’re just awkward and in the middle. The other thing you could try is a power nap instead of her full second nap - so aim for one main nap but let her sleep 10-15 minutes in the pram if she can’t quite make it to bedtime. That will take the edge off the tiredness but won’t relieve the sleep pressure which is what she needs to sleep soundly at night.
I also find my DD’s cry is totally different if she’s awake and cross about it than if she’s in pain. Then if ever I’m not sure - if I pick her up and she’s in pain she will carry on crying and writhe around, whereas if she’s just awake and not happy about it she’ll calm down straight away. It may have been pain keeping your DD awake, but given the length of the wake it may also have been that your DD just ran out of steam eventually and went back to sleep.
As for the medication - if you give a dose of painkiller once a day for three weeks you will do your baby absolutely no harm at all. In my opinion it’s better to give painkillers than not. Babies can’t tell us what’s wrong so if I think DD is upset because of pain at nighttime (when distraction, going outside, or chomping on a toy aren’t options) I always give her some medicine. As your DD gets older it will be easier as she will be able to tell you what’s wrong so you can make a decision about whether she needs painkillers. It’s really just in the short term, when they’re pre-verbal, that you might give painkillers when they’re not absolutely needed. But better that than letting her suffer inadvertently, I think.
I hope this is helpful. The nights are an absolute killer.