Rather than a walk-in bath and shower, you may decide a bath lift is the solution for your bathing mobility problems.
You could try a bath hoist, which could be operated electronically or manually. A manual control, however, could be straining for your carer and also prevents you from bathing yourself independently if you are capable of it.
Electrical bath lifts may be portable, inflatable or fixed in place. One benefit of an inflatable bath lift is that it can set you down to the very bottom of the bath, while portable non-inflatables will keep you suspended a little way above.
You may also consider a fixed belt lifter, which has the advantage of keeping the bath easy to clean. However, if you are not sure of your balance, you will need to install hand rails to hold on to as well.
Compare bath lifts with Mobility Compare to help you decide which one suits you best.