Yes, that does sound like finrot to me, but are the fins splitting or getting ragged round the edges or just going white? Are there any red streaks in the fins?
Also, have you checked the water params, and if so can you post them here?

If the finrot is not yet severe then salt (at a level of 3 tsps per gallon) may well be enough, combined with perfect water quality. If the finrot is advancing quickly however or mollies won't tolerate a higher salt level, then start with a good antibiotic med - something like Maracyn and Maracyn 2 combined - but keep an eye on your parameters as these meds will affect the cycle. (If you can treat them in a hospital tank, that would be ideal). Finrot is usually bacterial in origin, but poor water quality is often the trigger so you might want to check that. If you do use an antibiotic then do a large water change to get rid of most of the salt first.
Hope this helps.