Yes, you can ask your interior designer to tag along when you are buying lights and bathroom fittings for your home. In fact most interior designers have collaborations with certain bathroom and lights shops.
However, most interior designers juggle a few interior jobs at a time and might be difficult for them to accompany you. So make arrangements with your interior designer early so that they are able to cater time for you. They will be able to advise you if the fittings that you have chosen are suitable for your renovation style and if the fittings are able to fit into the intended spaces.