This sounds a lot like us, and we are still having problems eleven months later. This is not to scare you, but to hopefully encorage you to follow your gut feeling and demend referral if you feel your baby needs it. I was sadly fobbed off by the bf clinic, hv, GP etc., until we demanded a referral, and thankfully we are now being properly treated for reflux.
The advice your hv has given you is dreadful...if your baby is refluxing feeds, formula will come up too...and is actually more likely to make it worse as it doesn't digest so quickly.
There could be underlying issues as mentioned, such as tongue or lip ties, a cow's milk protein allergy or intolerance, "simple" refluxing that your little one may or may not grow out of, etc.
What are feeds like? Do they take a long time? Does your LO seems satisfied afterwards? Any arching or discomfort? What are the poos like?
If you get referred you might be able to get hold of breast milk fortifier...I wish I had been given this option instead of chucked on high calorie formula.
It's really improtant that a number of things are checked to make sure your baby is feeding efficiently, so definitely get to a bf cafe. If they aren't feeding effectively they will be burning more calories than necessary to receive their food, which just compounds things when they chuck it all back up!
If you are using gaviscon, you could ask to try carobel, which can be used when bf as well. It's a thickener also, but will add a few calories to each feed too.
Definitely get referred if you feel that things aren't right. There are lots of people in your boat, so don't worry about being alone with it. X