So I accidentally removed all my mods After overcoming my sadness and wasted time, because I heard that once you remove a mod, you can't get your things back.
Just making sure that that's the case?

I see no reason why you can't just reinstall them. Wrye Bash will show you exactly what mods you had installed for any save game, no reason to lose any items or quest progress.

Well, you can always reinstall them, but other than that, there's no magic "Undo my dumb mistake" button.

I didn't realise that I had deleted the mods, and then played the game again. So if I reinstall them, will the items I left in things such as drawers still be there?

They will if you load a save that still has those mods active (once you reinstall them). If you have already overwritten all your saves without your mods loaded though, that's irreversible. When the game prompts you saying that the save is missing content, you should pause and think about why - especially if you weren't expecting that.