how to add few music files to iPhone which is "manually managed" by a different PC?
If you are manually managing via iTunes, there is no way to just add some songs to your iOS music library without deleting what is already there. 
There are a couple workarounds that are only slightly unpleasant. 


Use a iOS ripping software like the one by iSkySoft to copy the music from your iOS device to the computer, add that to the iTunes library of whatever computer you have, then sync all of that plus the new stuff. [40% unpleasant]
Put the songs in a cloud service like Dropbox or Box to store, and listen using the appropriate app. [10-25% unpleasant]