You are correct that inspection,
iyun, is a very important part of the
tevilah process. The assumption is that during cleaning and removing barriers, you will not move on to a subsequent area before checking that you have finished what you have cleaned; that in itself is a type of inspection.
During your shower, while finishing your cleaning, you should run your hand lightly over your body to check areas not visible to the eye. But again, this need not be exhaustive or too nit-picky, given that you can rely on what you saw during your cleaning process. A visual inspection of your body, directly or in the mirror, after your shower completes the process. Thus, the inspection you describe is quite adequate.