There doesn't realy appear to be any outward signs of disease other than the fins.
I would test the water and make sure the parameters are ok. There should be 0 ammonia/nitrIte and nitrAte should be below 40. The temperature should be within reason as well and there should be no major fluctuations either in temperature or in pH. This looks like a water quality issue to me.
Another possibility is internal parasites. Do you know what it's poo looks like
? If it's white and stringy you'll need to isolate and treat for internal parasites.
Possible ways to help the fish would be a large water change with dechlorinated water (as always) and, if the other fish/inhabitants will allow for it, a little salt. Alternatively, isolate the fish and ensure that it is in perfect water and add a tiny bit of salt and watch for any more symptoms.
I should also mention that I am not familiar with 'golden' rams so I cannot say whether it's color/appearance is normal or not but it's finnage is clearly unusual and the behaviour you described points towards a problem.
edit: Though everything points towards a water quality or disease issue, the shyness could also be due to unsuitable or overly-boisterous tankmates. However, the tetra and heavy planting would suggest the tankmates are quite peaceful...