Your not weak.
I think just by looking what you wrote here, that your pretty strong.
Ive seen many people trying suicide in these situations and by seeing that you carry on is something great.
(Id recomend you to visit a psychatrist tho.)
Remember that online tests CAN give wrong results but it can be helpfull at times.
And your mom just tries to encourage you to try harder in her way, she simply gets upset by seeing you being sad or frustated.
I believe she has a really hard time too aswell.
Dum spiro spero (as long as you live, keep believing).