If you switch to another solicitor you will have to pay the current bill, and your new solicitor will have to try and include this money in the total claim.
There is no guarantee you would get that money back though - especially if the new solicitor duplicates the work. The other side cannot be expected to pay two lots of costs.
What is the problem with the current solicitor? The wheels of justice turn very slowly indeed - is it the length of time you are waiting to see a doctor that is the problem?