We tend to go with calendar date - just easier and its an average/approximation anyway, with the idea that some LO's need more or less A time.
She's 5 months or thereabouts? You've got the right idea in my opinion - I'd start off with 2.5hr first thing in the morning and after a good (1.5hr+) nap and 2hr15 after a short nap (2hr max. if nap is 30min though).
re: meds - I'm not a doc or a pharmacist, best ask a pharmacist for that info specific to your situation. What I say is that if LO is in pain that's preventing them from sleeping, you can't expect them to sleep well - if I had a toothache and I couldn't sleep, I'd take pain meds, yk?
You could do a gradual withdrawal/shush-pat sleep training provided you're not expecting her to 'get it' in 3 days... Just gradually put her down less drowsy and comfort her off to sleep in the crib. Eventually you will be able to reduce the comforting in the crib and she'll learn to sleep on her own but best to take it really slow if you want to sleep train while she's teething.