I am sole caretaker for my wife, age 88, who has multiple health problems. Should I feel selfish?

You are not selfish to place your wife in memory care to get your life back. Then visit her as your husband, not a carrgiver.

There comes a time when caring for a dementia patient that we miss our life and the workload is too heavy. If she is memory care eligible I do not see why you should not do it. Be aware it is not a perfect solution. It comes with it’s own issues and it did not come without some guilt for my family. Expect calls and her to still require many needs to be met. Good Luck.

"Should I feel selfish?"

I don't like questions like these, because basically it's fishing for compliments. You're trying to provoke certain answers with that question.

As for the rest, your situation, you're the only one who knows what you're going through and how your wife is. You decide what's best (memory care or not), not strangers on the internet who don't know the full picture.

Absolutely not. You need a life too and your wife would have good care in a MC.

If your wife's care is truly getting to be too much for you, then perhaps yes, it's best to start looking for the appropriate memory care to place her in.
If it's just because you're not wanting to be tied down to caring for her 24/7 perhaps you can find an Adult Daycare Center in your city to take her to up to 5 days a week and up to 8 hours a day. They are fabulous and take great care of the folks that attend. They give them breakfast, a snack and lunch, plus keep them occupied with various activities.
Or you can hire some in-home help to assist you with her care.
That would give you ample time to play tennis, and do whatever else you would like to do.
You will know when it's time to place her. When it's best for you both.
Best wishes.

Nothing selfish about wanting to put her in MC, you can return to being her husband not her caregiver.

Take your life back, know that she will be safe. You can visit her as much as you like,

I wish you the very best and know that you will be making the right decision for the both of you.

Please don't hesitate to place your dear wife in an appropriate facility... when you have been carrying the caregiving burden a long time you may not realize how much it has weighed you down until it is lifted.

I would say at age 90 with excellent plans in place to keep yourself active physically and mentally that you are absolutely right to consider memory care for your wife. You can still visit often, but will keep yourself healthy, which is what she needs most. At least look into respite for the times you are gone for long periods of time and a day care facility for when you play tennis.