As beeblebrox says, ask your teacher to clarify. He/she has probably seen many students go through experiences like this, and is in the best position to know what is the best approach for you at this time. My teachers have always emphasised that when strange, interesting, etc, experiences happen that it is very important to remain mindful of what is happening (not go off into a dreamy state). So stopping and checking what is happening may well be a good thing to do.
You are fortunate to have a teacher who has good experience with what you are experiencing. My advice it to trust his/her advice and see where it leads.
By the ways Chanmyay Sayadaw mentions this sort of thing here: http://www.buddhanet.net/imol/vipcours.htm
That's what the Buddha said, you can attain long lasting concentration by means of walking. So when you are aware of each individual movement of the foot, and sometimes the intention too, then the mind becomes gradually concentrated on the movement of the foot very well. And the more energetically you note the movement the more deep is the concentration of the mind. Then when concentration becomes deeper and deeper you feel your feet become light as they automatically lift, automatically push forward, automatically drop down. You come to realise it. Sometimes you get startled at the experience of this automatic lifting and pushing and dropping of the foot. and as soon as you feel it you say to yourself, `Hah, what's that? Am I mad or not?` In this way you get startled at the unusual experience of the movement of the foot.
When I conducted a meditation retreat in England at the Manjusri Tibetan Monastery, the Manjusri Institute in northern England near the border of Scotland, one of the meditators had put much effort into his practise both sitting as well as walking, and awareness of the activities too. So after about four days meditation he came to me and asked a question. ''Venerable Sir, my meditation is getting worse and worse,' he said. 'Now what happen to your meditation?' I asked him. Then he said, 'When I am walking one day, Venerable Sir, then gradually I am not aware of myself. The foot itself had lifted, and it itself pushed forward, and then dropped down by itself. There's no I or no me, no self, no myself. Sometimes though I control my foot, the foot doesn't stay with the ground. It lifted by itself. Sometimes it pushed forward very long. I couldn't control it. Then sometimes it's getting down by itself. So my meditation is getting worse and worse. What should I do?' Then eventually he said, 'I think I have gone mad.' Such an experience was very amazing.