I feel so guilty about placing my mother with severe dementia in long-term care. Did I do the right thing or am I being selfish?

Yes. Most people do not have the knowledge, skill, or resources to care for someone with dementia. Putting this person in a facility where they can get this help is a kindness. It shows how much you care for your loved one.
Right or wrong . It would also be selfish to keep elderly, medically illed parents home without having the ability and availability to provide them with proper care and attention, though it might make us feel less guilty.
Tough decision. But knowing our own limitations is a strength, not selfish. I have seen families that stretch beyond their limits, ending up hurting themselves and their loved one. Driven by blinding guilt, they fail to appreciate the additional harm that they are causing. Asking for help, accepting help are healthy and wise. Caregiver depression is a major risk. I am sure your mom wants you to stay healthy.