dinks sorry about the issues your little one is having. Formula is very very unlikely to be the answer - it can make reflux worse in fact. It's harder to digest, hangs around longer in the stomach (more opportunity to reflux therefore), and is usually drunk in larger quantities than breastmilk. Also, the action of bottlefeeding does not stimulate the gut to move food through in the same way as the action of breastfeeding does. Can I ask a few questions? Might make our advice on here a bit more useful to you!!:
What are the symptoms which make the docs/ HV think reflux?
How's her weight gain? How often's she feeding?
Have you ruled out oversupply issues as the cause? This can make babies vomity and fussy and can be remedied by block feeding (think this if your DD has predominantly green nappies, is absolutely stacking on weight, and feeds frequently but very quickly).
Do you think she could have an issue with cow's milk? Proteins consumed by the mother can pass into breastmilk and cause upset in the baby. If she's got anything like eczema, mucus in her poo, or a red rash around her bum that's not nappy-related, then this could be an issue.
Has your DD been checked for a tongue tie? This can cause air swallowing, vomiting, trouble feeding, poor weight gain, etc. Easy to remedy if it's present.
Given you're breastfeeding, I think the best thing you can do at this stage is to contact a qualified lactation consultant (LCs )who'll come and talk through things with you. This website has a list of practising LCs - some charge, some work for the NHS.
Hope things get easier for you soon, and if you're sure it's reflux and the gaviscon's not working, do go back to the doctors as there are other medicines that can be given - e.g., ranitidine, acid-blockers like Omeprazole. Re. administering gaviscon, have you tried using the syringe from the baby neurofen bottle? It's got a bigger-than-normal hole so won't clog, and you can squirt it into your baby's cheek after a feed.