We can use present simple to talk about
- something that is true right now
- something that happens regularly
- something that is always true (a permanent state)
- something that will happen in the future.
We use present continuous to talk about a situation that occurs continuously for some time before and after now.
The first meaning of present simple is usually only used with non-continuous verbs: ones where you don't use present continuous to describe the current situation. These tend to be verbs where can't see the person doing anything, for example want, like and fear. A small number of verbs are mixed: one meaning may be normal and the other non-continuous. An example is think, which is used in present continuous to describe the process or thinking and in present simple to express an opinion.
I am thinking about quitting my job - process: present continuous
I think that we are nearly finished - opinion: simple present
Feel is very unusual in that
...there is no real difference in meaning between "I don't feel well today" and "I am not feeling well today. www.englishpage.com
You have made it clear that the loneliness is not a permanent state but a temporary thing, nonetheless feeling lonely isn't instantaneous, so it is quite OK to use present continuous to describe your present emotion. It is also reasonable to use present simple to describe your emotion at this exact moment, even though it is neither an instantaneous emotion nor a permanent state.
The response is therefore perfectly OK, and your alternative is also OK.