You dont need to get permission or anything from your HV to change your LO's milk.
However, I think that hungry baby milk probably isnt the answer. Your LO might seem hungry a lot because he's not keeping it down, even with hungry baby, if he doesn't keep it down he'll still be hungry and hungry baby milk is harder to digest so may upset his stomach more.
I had the same dilemma with Brady at around the same age because he was/is a very sicky baby. A lot of the problem was that he was taking in too much air which was getting trapped so the milk just came back up. I changed to Dr Browns bottles and do various exercises with him in the morning and evening to get the wind out.
I did change his formula, originally we were on SMA, then tried Aptamil, Aptamil Comfort and finally settled on Cow and Gate which agrees with him much better.
You should be aware as well that hungry baby milk can make them constipated because its harder to digest.