I agree with the advice to have the ends of your floor joists resting on
concrete block walls, not just supported by them as would be the case
with a header.
Also, you need blocking between the joists. The whole purpose of
bloking between joists is to prevent the joists from twisting under a
heavy load. By keeping each joist vertical, you maximize the rigidity
of each joist and hence the whole floor.
Really, while you very well could do the physical work yourself, this is
not a DIY project. Your house is your biggest investment. Don't put it
in jeopardy by designing the addition yourself as well. You need to get
an engineering and/or architectural firm involed in designing the
addition so that what you build will meet the building code and be safe
to live in.