Probably you need to take your O levels privately (work really hard)
and take a diploma in Nursing at Nanyang Polytechnic, Ngee Ann Polytechnic . But however you are required to have experience at the same time if you want to do part time.
You require to be very strong in your mathematics because O level is really different.
Due to your N levels result, i dont think you can go in, except business, culinary or engineering (like what he said).
It is really important to never fail your mathematics. It serves as a foundation to your Nitec and Higher Nitec so that can do calculations and stuff.
So,
OR
You can take the following Nitec Equivalant Courses to Enter which they also require mathematics to be passed. (which i am sorry to say you can't take).
OR
Take another course in Nitec from different school then graduate to higher nitec and switch to school of Health science (Related courses to progress in to Diploma in Nursing)
The route is very long but fret not, i studied in ITE for 3 years for Nitec and Higher Nitec and i am currently studying Diploma in ITE and it has been a great journey for me, i know you fear about your future but it is really not the end. I was a NT level student too and i had the same fear as you.