Since this is a school assignment, I suspect the solution is expected to be simple, not industry grade. The simplest bootstrap that works for the high-side N-channel MOSFETs looks like this (half bridge shown):
This is from a textbook by Grant and Gowar.
Now since you're not given any PNPs, you can't have the complementary pair drive Q3 there. Instead you have to use a two-NPN totem pole in their place.
You seem to be given all the logic gates you want, so this looks like will satisfy your assignment requirements.
A bit more searching even found (in an article referenced by Grant and Gowar) something more economical along the lines I was talking about:
I have no idea why you're given "Infra-red Detector" and "Infra-red Emitter" but if by any chance that means you're given optocouplers, you could also do this:
You're not saying what kind of motor you need this H-bridge to drive. The above circuits are suitable for BLDCs or motors where the on-time of the high-side switches cannot be arbitrarily long because the capacitor can only recharge when the high-side is off (it's shorted while high-side drive is on). If you need arbitrarily long on-time, then a slightly more complex circuit called a charge pump is needed to continuously top off the boostrap/tank capacitor. The textbook-level circuit is (only the high-side driver is shown):
Again you'll have to substitute the complementary pair to meet your design requirement of no-PNPs-allowed. This circuit also requires a clock signal (square wave generator) to drive the pump, which you can make in many ways with what you've got, e.g. op amp. If you don't know how to do that bit (and you need it), you should search the site and/or ask a separate question.