Based the on the description of the sore at the base of the fin, I'd say you have a bacterial infection. However, to clarify, that would be considered an external infection. Treat the tank (if you can isolate the sick fish in a small tank, that's best) with a wide-spectrum antibiotic. I've had great success with erythromycin (at 2x or even 3x the recommended dose in bad cases). Some of the furan-type antibiotics may also do the trick. Additionally you can use acraflavin drugs, they work well.
The white ball on the fin can be parasitic, bacterial or viral. Without seeing it I can't say for sure. If it's viral (lymphocystis) then there's not much you can do as there's no cure. It will come and go as the fish ages. Sometimes it vanishes forever, sometimes it gets so bad the fish dies. If it's a parasite, try one of the several formalin based remedies, they do a good job.
If in doubt, treat for parasitic and bacterial issues at the same time. Most medication producers will clearly state on the labels if the meds can be used in conjunction with other meds. Read the labels for the active ingredients, that'll help you choose alternate brand medications to use together if you can't get different meds in the same brand.
This is all my opinion and based on my own experiences. There may be other, more experienced aquarists here with more years keeping fish than I have who will offer better recommendations.