I think my voicemail was full and now there are simply no voicemail icon when I pull up my phone functions. I’m not sure how to get it back or how to delete old voicemails to make room because I don’t have access to it anymore.
If you have carrier voicemail:
An example from my carrier:
Call voicemail box xxxx and press 11 for the main menu / option
Unheard messages are stored for 8 days. Messages you've listened to will be gone after 24 hours. Longer storage is also possible. Press 5 while listening to your message and it will be saved for 7 days.
The voicemail settings are controlled by the carrier.
Do you use Visual Voicemail messages, see this Apple article: Check your voicemail on iPhone
Check your voicemail on iPhone – Apple Support (AU)
Try to free up iPhone device storage see this Apple articles below:
If you need more space for an update on your iPhone, iPad, or iPod touch
If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support
How to check the storage on your iPhone, iPad and iPod touch
How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)
Clear Other storage on your iPhone or iPad
Clear Other storage on your iPhone or iPad - Apple Support
What's the difference between device storage and iCloud storage?
What's the difference between device storage and iCloud storage? - Apple Support