You could persevere with the bottle by removing the lamb from its dam completely, but it is difficult. I have found in the past that both lambs and kids start eating a mixed concentrate (as opposed to a pelleted feed) quicker, adding something like readigrass as well as offering very fine hay should help. Also if you can access real milk (doesn't need to be raw, but shouldn't be homogenised and preferably goat rather than cow - not sure if you can, goat keepers nearby?) rather than using powder/milk replacer it may be a lot more like the dam's milk and the lamb may take it easier.
It is unlikely that the ewe is going to improve if she is being forced to feed the lamb while she is sore, and she may already have very little milk.
But it is really difficult to advise for this kind of problem.