I have had pressure in my right ear for about a week. Little to no pain, but constant ringing. What do you recommend?

You have what is referred to as "aural fullness" and it can be a symptom of several underlying causes such as illness, allergies, temporary pressure changes, etc. Since this has lasted for a week, it is time to make appointment with your primary care or ENT. If you know you had an illness recently causing head pressure and are recovering, it can take up to 8 weeks for that fullness to clear up. If you had no symptoms of an illness, I would visit an ENT to explore the causes further.

Alexandra provided an excellent answer. I would add that in my experience, the most common causes of that "full" feeling, in conjunction with ringing, are wax build up and fluid behind the eardrum. If you have previously had to have wax removed from your ears, and suspect that could be the issue, you can try an ear irrigation kit from your local pharmacy. I would highly recommend using their drops overnight to soften the wax and make it easier to irrigate the next day. Now, if you are wondering if the fullness is fluid behind your eardrum, I would ask if you have had any allergies or colds lately or if you have flown or been swimming. If you can't pinpoint a single one of those, then wax is the more likely culprit.  Of course, seeing an ENT is the quickest and safest way to get your answer, and if it is wax they can remove it, and if it is fluid they can potentially help you treat it. There are other causes as well, but these are the most common that I see.

VERY IMPORTANT to have a full diagnostic hearing test ASAP followed by an ENT Specialist consult. All the best. Lisa G