Sounds like you need a setup on your steel strung guitar. You say you don't play barre chords often - that suggests that you are using the first three frets most of the time. Frequently the action at the nut is higher than ideal; this means added pressure is needed particularly at fret 1.
Your problems coincide with the change of guitar it seems. With a good setup the steel strung guitar should be very little different to play to your nylon one.
Another possibility is that your holding of the smaller guitar is less secure, resulting in using the neck as a handle. Make sure that you can hold the guitar securely with your arms/body without having to grip with your hands. If your grip on the neck is tight, your hand will be subject to constant strain.