I've heard some bad things about t-cut (contains ammonia?) so you're right to be looking for an alternative. I've used Autoglym super resin polish to quite good effect, but it can take a few attempts and plenty of elbow grease. The Meguiars swirl remover is great, and I seem to recall they also do a scratch remover too that works well on scratches. However, if you can feel them under your nail then I'm not sure that you will improve them much by hand.
If they are quite bad, maybe it's worth asking a decent valeter for a quote on machine polishing the paintwork for you? At least that way you know that you've got a great surface to look after and protect from there on.