I want to draw on any app pdfs, videos, code. It would be helpful to aid in demonstration in a class setting for me. Do you know if any such app exists that does not require an external pen i.e. using mouse or trackpad to draw.
Check out Snappy App - it allows you to grab any part of your screen and float it above the screen - then you can draw on it, change its transparency, shrink it down, whatever. There's a free version which does more or less all you'd want and the in-app purchases are very cheap (you need an in-app to draw on things). I've also just recently been introduced to https://presentify.compzets.com/ which takes a different approach but might also meet the requirements.
This software does exactly that http://ink2go.org/ allows the user to draw on any application. It also allows for screen recording and other features. I suggest if you are looking for other alternatives to search for "screen annotation software for mac" that gave me more precise results.
If you are looking for a screen annotation app that is unobtrusive and fast, check out DemoPro . DemoPro lets you configure hotkeys to draw on the screen, which is very convenient if you are doing live demonstrations. It also includes a countdown timer which can be useful for breakout sessions, exams, etc.
Screenink is also another app that will take a screenshot for the moment and allow you to draw on that, annotate and save.
A friend uses Highlight.
You have to define your own hotkey to turn it on and off.
I've been looking for a nice mouse highlight tool for 2 hours and find something different but really nice!
With the free version, you can easily draw on your screen and also highlight the screen with the shift key.
If you're still looking for a cursor highlighter I've found Mouse Locator App (http://www.2point5fish.com/)
But it's not very polished and has few configuration options
When I found Screenbrush it already made my day and stop searching, but I read on a forum post somewhere that if you change your search query to "mac Screen annotation software" you will have more results, maybe it helps in finding a better Cursor highlighter app.