I want to know if there is any way to modify my Facebook profile so that no other user can click on my photos tab and see other photos. Within the condition I'm outlining however, I could still see all the photos I'm tagged in. Also within this condition, it would not necessarily be removed from my timeline so the response "click hide from timeline" would not suffice.
You can set the privacy of all your photos by customising who can see each album. Go to the album and click on the symbol next to the description of the album. If it's public it will be a globe, if friends the symbol will be two person shapes, if customised already it will be a gear symbol. You can use this menu to change the customisation so that only whomever you want to see it can see it, if this is just you, then select "Only Me".
You don't have the ability to control the privacy of photos that other people upload though. The best you can do is not be tagged in them. You already appear to know about the control for this.
Remember that you can view your facebook page from the perspective of another user to see if the settings you have put in place have done what you want. To do this, select the View as option from the menu in your cover picture:-
This will initially show you the public view and then you can change to see it from the perspective of a specific person by clicking on the link at the top of this view:-