Chili and bell pepper substitute due to allergies?
You are not going to find anything outside the chili family that gives quite the same flavor, so substituting flavor-wise is not going to be possible.  Note that paprika is a spice ground from particular pepper, so if you are allergic to all capsicum peppers, you don't want to use it.

What you can do is build other flavorful combinations which you enjoy and which you can eat.  Some things to consider that bring a touch of some type of heat with them include:


Mustard powder (a touch of mustard-type heat, and a deep flavor.  Probably want to combine with some herbs like oregano or rosemary.
Horseradish (just a touch for piquancy)
Ginger, which will work very well in Asian inspired dishes, and in combination with those flavors
Szechaun peppercorns (not a capsicum pepper) -- they have a unique flavor and effect; you will have to decide if you like them


All of these flavors are "hot" but from different chemicals than the capsicum peppers, so they will all have different effects.