It's a possibility that the regrigerator's conpressor is low on oil, this could cause the issue you're describing- being "loud" or "noisy". Being Low on Refrigerant can also cause this sometimes.
To directly answer your question, sure you can do something about this yourself as long as you're familiar with refrigeration systems, and have a set of gauges to check the refrigerant level, etc. The oil and refrigerant must be installed precisely and if you add to much(or too little) that'll be a problem.
Usually when a refrigerator gets noisy, especially if it's several years old, just replace it. Check your local Craigslist page as there are always deals to be found on there for nice, used appliances. You can call a local appliance shop, one that sells used ones, to see if they have a used one for you. Also, the Facebook Marketplace is a great source for stuff like this.
If you have a friend or family member, who works in the hvac Trade it couldn't hurt to ask them to come check it out for free or perhaps a minimal amount, you can try it but 99/100 times you'll end up buying a new refrigerator refrigerator
.That's another good thing about Craigslist & FB Marketplace- the option to barter or trade is often available.
Another option if you’re not comfortable with a used one is to call the local stores that sell appliances, like Lowes, Home Depot, Best Buy, etc. and ask about a returned or blemished item, usually they include a full warranty identical to a new one at a much cheaper price!
My Refrigerator got loud a while back and I had another one the sane day for $50, it was on Craigslist!