Your bed is possibly 3/4 size, which is designed to accommodate a 48" wide mattress. Some of the second tier brands will still make a 48" set. Second tier does not mean second quality. Just means their name doesn't start with an S.

If you want to use a full size mattress, what you need to do is find an old mom-and-pop furniture store that also sells mattresses. Call and ask if you can purchase a "modi plate" from them. This will allow you to bolt rails to the plate, and then bolt the plate to the headboard and the footboard. You may want to consider a steel rail since its narrower and will probably get covered by a dust ruffle or sheets anyways.

Good Luck

It depends a lot on how the existing are hooked in and how much wiggle room you have. If the side rails are wood, the usual attachment is pin mount

If you can squeeze another 1.5" from the headboard / footboard, you may be able to remove them and retrofit a surface mount