Elana,
No! You are not weak.
It is actually quite strong and commendable to take care of yourself in this way - not everyone can do so.
Maybe you will be ready to take on a full time job, but it is wise to start part-time at first until you adjust. It is a big adjustment, physically and mentally.
And your T is right - it is their responsiblity to make sure the work gets done.
Not something you need to worry about at all.
Well done!