LEGO’s Pick-a-Brick service has only a limited amount of the total range of pieces ever produced. It contains a subset of the pieces available in current sets.
The Bricks and Pieces service (on the LEGO website under Customer Service) has a slightly larger range of pieces, but still limited to those that are currently produced by LEGO. This service is unfortunately only seasonally available (during busy seasons it goes offline).
For a broader range of pieces you have to go to third-party websites. The main ones are:
Bricklink: This site contains all the pieces ever produced by LEGO, and provides a marketplace where sellers all over the world sell these pieces either New or Used. Depending on the age and rarity of the piece, prices can be quite high or sometimes way cheaper than what LEGO charges. Just beware that shipping and handling costs are added on to your order, and those costs vary from seller to seller. Also, BL uses slightly different nomenclature for pieces than LEGO does, but searching by mould number (the little 4-6 digit number printed on each piece) should work. The rim you mention is this piece: Wheel 30.4mm D. x 20mm with No Pin Holes and Reinforced Rim and its listing shows all the tires that fit with this rim.
Bricklink has a competitor called BrickOwl, which offers a similar service.
Finally, you can also look for specific pieces in lots listed on auction sites such as Ebay, as they sometimes contain pieces you need at lower prices (especially when part of a bulk lot of other pieces that might be useful for you).