Hi when I started playing polo I got elbow pains as well which I believe to be tennis elbow. For me it was nothing to do with the paddle it is just throwing of the ball. I know this as I now wear a support for my elbow which has completely solved any pains I was getting, However I don't wear the support when I do other types of paddling (white water, play boating and sprints) as I have never had any elbow issues with any of these. But I do need the support when I play squash which is how I determined that it must be the throwing involved in polo not the paddling.
I've linked the elbow support I use below its not the cheapest but it works really well, doesn't loosen when wet and can wash it in a washing machine which is important if you are using it outside.
Hope this helps