First off golfer's elbow is on the medial aspect. Eccentric contraction seems to be what everyone is jumping on for tendonitis/tendonosis issues as far as active rehab goes.
That exercise has done well in both clinical trials and patients that I work with that have lateral epicondylitis, but it doesn't sound like you have that. I know everyone likes picking up heavy shit on this site (myself included) but try some eccentric band work with the pronation and supination and if there is any adhesions or scar tissue in the offending muscles get that worked out. Ice is nice, and I prefer taking bromelain on an empty stomach to deal with inflammation.
I urge you not to 'work through the pain' as this will probably set you back further. I personally would rather spend a week or two fixing the problem then be set back for a longer time further down the road because I tried to be a tough guy.
Sorry so vague, and nothing personal, but I prefer to be hands on when I give advice. Nothing against your self-diagnosis.