You can ask though! Always ask. Court fees yes, other fees, maybe.
Ask for them all. Simply state, after asking for the damage amt for +court costs, +lawyers' fees, +other fees (since these wont totally be known yet leave them as an undetermined amount until trial is done).
You said "if I win"...if you did not ask for them win your initial filing, you can request to amend your complaint (maybe) to include these. If you cannot amend your complaint & you did not ask for these charges, judges will usually not allow you to tack them on later.