Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain aching of gums below the root canalled teeth can be due to re-infection in the root canal treated teeth but in case if even the upper gums pains and
cold water relieves the pain there is more of a chance that there is inflammation in the gums secondary to infection and it is the cause for pain..
Sinus infection can lead to pain in upper jaw gums and not the bottom jaw gums as
sinuses are present in close proximity with upper teeth..
Nothing to worry, consult an Oral Physician and get evaluated and in case of inflammation in gums scaling, curettage followed by antibiotics, painkillers and topical application of gum paint will help..
You should also get an IOPAR[ xray] of the root canal treated teeth done just to check for any sprouting infection so that it can be cured before it exaggerates..
As of now you can take anti-inflammatory painkiller
Ibuprofen to relieve pain..
Apply numbing gel containing Lignocaine..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.