Yes...do make sure you can record in class. None of my instructors had a problem with it though one did have anyone who wanted to record sign a waiver basically stating we wouldn't sue her for anything she said in class that later turned out to be incorrect.
If you ask and an instructor says no, tell them you'd be happy to sign a similar document.
Watch the ads for Staples or similar stores, with back to school they often have some great discounts. I got a really decent voice recorder that has six "folders" (so you can sort your recordings by subject), the ability to download the recordings to an MP3 on your computer which you can then modify ("snip" segements if needed) or edit. It also is compatible with some of the commercial dictation programs like Dragon Dictation (not a cheap program but for someone with hearing difficulties this program can be a lifesaver translating spoken word to text). I wasn't able to use it for school (but that's not why I purchased it) but it also had a voice activated microphone so if you set up your recorder in the front of the room before the lecture/meeting started it would start recording once conversation began. A wondeful thing for some situations and less wasted space. (but you have the ability to edit with the enclosed program)
I was able to get the package for less than $35 on sale at my local office supply store during the back to school savings sales. You can also check out some of the smart pens that include recorders and can convert your written notes to typed text on your PC. They run around $100 but are useful tools for the right student.
Good luck as you begin your nursing education. And kudos to you for inquiring before recording...not everyone has such forethought.