No, it is not correct English to say "I feel painful."
You can say "I feel pain", or "I am in pain", because 'pain' is a noun, but "painful" is an adjective so you would need to use it qualify something else (as in your "I feel painful sensations" example).
If you must make that choice then it’s an ‘at-home service’.
‘A service at home’ would describe how, or in this case where the service was provided.
‘An at-home service’ would describe the kind of service provided. The fact that here, ‘at-home’ appears to describe how or where the service was provided is slightly relevant in semantic terms; not at all in grammatical terms.
The hyphen makes it easier to read and understand in some circumstances; harder in others. Either way, it depends on the meaning intended.
If anyone really thinks dropping the preposition in favour of ‘home services’ changes anything, doubtless he will be able to explain how.
If anyone really thinks ‘in-home… ’ instead of ‘at-home services’ changes anything, doubtless he will be able to explain how.
Why would you care that you actually have a company which provides services… either in the patient’s own home or the patients’ own homes? The differences are between right and wrong, not matters of choice, so why should you give a rat’s whisker?
Having written that kind of sentence for thousands of clients over many years, I suggest you let go of the whole idea and start afresh.
If you want to say ‘I have a company which provides services in the patient’s own home’ then say so… only don’t use such an unnatural form. Say instead ‘… which provides services in the patient’s home’’
Please remember one of the worst problems choosing words for such situations is that written speech is very much not the same as… ‘real' speech, for which reason do not plan on paper what you want to say. Get two or three colleagues together and record a real conversation with no notes or other aids.
Talk for long enough - which might easily be half an hour or more - that the process of talking with a recorder running stops being a barrier. Having achieved that, you will be recording what you think of as natural speech describing the situation in which you actually find yourself, instead of artificial speech purporting to describe a situation with which you’re not truly comfortable.
If you doubt any of that, try listening a lot harder to the average TV commercial, and asking yourself how authentic either the words or the delivery f those words really sounds…
Best Answer
I suspect feel like at home is a bad translation from some Polish phrase (this looks to be OP's "euro 2012 commercial", and it contains no English apart from having that title for the Youtube video).
I don't understand Polish anyway, but it's not obvious to me what a reference to home could mean in this context. Common idiomatic turns of phrase (definitely nothing to do with Euro 2012) are...
That second usage is normally "figurative". You can say you "feel at home with accounting software", for example, even if you only ever use it in the office. The point is you understand it, and are competent and familiar with using it.
EDIT: It seems my original link to "euro 2012 commercial" above is now dead. But here's another one which makes it clear that whatever Polish Sports Minister Joanna Mucha might say, the usage is probably best classified as a "glaring error".