So recently I completed all of Neloth's quests in hope to be able to join House Telvanni and live in Neloth's tower place, and after I dealt with his old apprentice he officially made me a member of the House, and said he'd get me a 'bed and chest'.

I figured that's what meant I could have residence there, but even after leaving the cell and waiting 10 in game days or so there is still no bed and chest for me. There are only two beds that are owned that were there all along. I even did the quest to fix the withered part of his house, but that only added a room with spriggans.

was I not supposed to get an actual bed or something? or is this a known glitch? I tried to find info on this, but I haven't been able to find anything.

I kind of need to know if this is messed up or not, because if it is and it probably won't get fixed then I need to start this character over and do everything all over again so I can live there, and I already did this one other time and I'm not looking forward to doing it again
any help would be appreciated!

I'm not sure about the beds (I didn't bother checking) but there is a chest that you can use.
It's not really near a bed, and it's in one of the little rooms full of cobwebs. Doesn't have the "steal" flag on it.

I own the home in Raven Rock, so I didn't bother investigating further.

You have to share the bed at the stewards house and the chest is in there for your use. I put a few misc. items in it to test if it is safe storage, but haven't checked it yet.

ahhh the steward's house works which is even better, thank you so much

You are quite welcome, m'lady.