Fascinating to learn about all these apps!
I remember Corel Draw being on school computers, and often getting old versions free on magazine cover discs, but never really being able to get my head around the node drawing tools at the time! But somehow that rainbow hot air balloon always appealed to me nonetheless...
I think I found the program I was thinking of though - PaintSpa Pro and PaintSpa for Windows! It looks like it was a particular tie in with RM computers, so probably in the majority of UK schools, but not popular anywhere else? https://www.thenimbus.co.uk/nimbus-software-titles/paintspa
It certainly has the texture pallettes, and it makes sense if there was a version on RM Nimbus 186 PCs as well as a Windows version on the Win3.1 RM 386 PCs!