I cannot update software on my computer.

If the applications that need updating are Apple applications that came with the computer, try going to the App Store Purchases tab or click on your profile and then go to Purchases to see if there is an option to accept the applications with your Apple ID. If that doesn't work, you can delete the applications and download them with your Apple ID. The applications are free. You may have to sign out of the App Store, restart the computer, and sign back in to download new copies.

Purchase History Review

This sounds like you your problem. See What to do when the Mac App Store shows a different Apple ID for software updates https://www.macworld.com/article/3267709/mac-app-store-apple-id.html. This document refers to a prior owner (use the discussion in it this is your situation), but is also applies to cases where a current owner's old Apple ID is the problem. The discussion below relates to the second possibility. 

Basically, If an app is purchased/downloaded using one Apple ID, then you can't update it with a second Apple ID. The app is inextricably linked to the first Apple ID. You'll have to delete it and purchase/download it again with the second Apple ID unless you set up family sharing (see below).

You can set up family sharing between the IDs to share purchases made with them. See:

Family Sharing  https://support.apple.com/en-us/HT201060

Set up Family Sharing https://support.apple.com/en-us/HT201088

You are welcome.