It strikes me as odd that your printer wouldn't accept third-party ink, Rosemarie. What brand was the old printer?
In January 2015, I bought a Canon MX-922 "all-in-one" inkjet and had no problem using a number of different third-party manufacturers' ink cartridges in it. I bought all of the ink through Amazon, bought only cartridges that specifically listed my model of printer, and paid about 1/5 the the price of the manufacturer's ink.
For any who might be interested, after two and a half years the print quality suddenly started to go downhill. I looked into buying a new print head but the cost was more than the cost of a new printer so I simply replaced the printer with the same model. I later found a video describing how to clean a clogged print head. I thoroughly cleaned the print head on the old printer (not a really quick process, but neither was it difficult) and put that printer into storage. I'm confident it would now work properly if I were to put it back into use.
As an experiment, I've only used the more expensive used Canon ink cartridges in the new printer and it still prints nicely. If the print quality degrades any time soon, I'll just clean the print head and go back to using the cheap ink. If it fails for any other reason, I still have the old one in storage to fall back on.