Can you apply for Medicaid specifically for long term care alone?

Yes, I just did it for my father. You are going to have to spend any money you have on health care or to the nursing home before you receive Medicaid for long term care though, down to about $2000 left in your bank account (that amount may vary depending on the state you live in).

Yes, you can apply specifically for LTC. Medicaid for LTC in a nursing home is a different program than "community Medicaid." If you look on this website under "care topics" there are a lot of good aricles about Medicaid and LTC.