Hi Heather,
High nitrites will cause fins to split, but the red streaks definitely sound like finrot has set in as well.
How high did the nitrites get by the way? Ideally they should never be allowed above .5.
If you use antibiotics like Maracyn/Mara 2 to treat the finrot it will affect your cycle and send the nitrites up again, which you want to avoid, so in the first instance I would suggest treating this with salt, which is usually very effective for finrot and won't affect the cycle. Add 3 tsps salt per gallon (subtracting a couple of gallons to allow for water displacement caused by substrate, ornaments etc.) in increments of 1 tsp per gallon every 12 hours - no faster than that. You can use any salt (except Epsom salts) as long as it does NOT have anti-caking agents in it. If you use aquarium salt then make sure it is just plain salt and doesn't have added buffers or tonics - those are more trouble then they're worth.
The added bonus of using salt is that it helps to protect the fish from the effects of high nitrites too.

You'll still need to keep up with the water changes to keep the nitrites down however, so remember to add more salt to compensate for whatever was lost in the change, e.g. if you remove 2 gallons of water, add 6 tsps of salt to the new water going in.
The salt should start clearing the finrot pretty quickly; when the red streaks have gone and the fins are not splitting anymore then perform water changes to slowly clear the salt out. At that stage you can add Melafix to speed the healing process.
Hope this helps.