First of all, see how much the combined DLC will cost. If it's less than the price of the ultimate edition, you might just want to consider buying the full game again for your convenience. I recommend the GOG.com version because it has no DRM (e.g. required online checks) and it includes absolutely everything, including some items that used to be timed exclusives: https://www.gog.com/game/dragon_age_origins
I'm not sure if it's still possible to buy the DLC separately in case you have a physical copy, but it it works, go ahead.
If you can't buy DLC separately, then try to register your physical copy's product key in the Origin client and this should give you a digital copy of the game as well. Then you should be able to buy the DLC on Origin. (That's what I did with my physical copy and I haven't seen the disc in years. 😛 )
You can then download and install the game plus DLC from Origin. If you don't want to reinstall the game, just leave Origin alone after buying the DLC and you can get installers over here: https://help.ea.com/en-ca/help/origin/origin/download-dlc-for-classic-origin-games/#dragonage
As long as you're logged into the game with the same account you used to buy the DLC, then they should work.
Note: Most of the DLCs are in dazip format. To install these, you need to use DAUpdater.exe, which you can find in the folder where the game is installed.
This is all a bit convoluted, so feel free to ask any followup questions.
