Those first 6-8 weeks can be so hard as your LO is having what seems to be back to back growth spurts and your supply is being established.
I know it doesn't really make you feel better right now to hear that what you're going through is normal and not unexpected, and that it does get better, but it is, and will and usually between 6-8 weeks. Feel free to want to punch me now because you're exhausted, sore, wrung out, and want it to get better right now! I know I sure felt that way at that point, and here I am now past 9 months, still nursing and with no intention of stopping any time soon!
Onto the topic of formula. This is one of those that is and always will be hotly debated i think, but an educated decision is always the best decision.
The first thing you need to decide is how important it is to you for your child to only receive breastmilk exclusively until you wean onto solids (WHO recommendations are until at least 6 months exclusively, up to a year before introducing cow or goat milk, and up to 2+ years, which in all honesty is not common in western society, but there are what seems to me to be an increasing amount of breastfeeders these days who nurse through until at least 1 year. Your consultant is correct in that introducing anything other than breastmilk into your LO's digestive system drastically changes the natural flora and normal state of the digestive system. Again, how important that is to you is a personal choice.
Whether to introduce formula periodically or only occasionally is, you guessed it, a personal choice. While some women can supplement fine, for many women it is the beginning of a downward spiral in not managing to establish and maintain their supply and breastfeeding relationship.
The not full feeling of your breasts is perfectly normal once your supply begins to establish and the initial engorgement settles. If your LO is gaining weight and you are changing plenty of wet nappies, your LO is getting "enough." Because breastmilk is easily digested, and your LO is able to more effectively absorb the nutrients and nourishment from breastmilk than anything else, not pooping for days (up to 10) is not uncommon. Your breasts don't run out of milk and will produce more on demand, which is what your LO is doing with the constant suckling right now by letting your body know how much he needs so that it can meet those demands more readily. As they grow, there will be periods again of increased nursing to build supply to meet their growing needs.
Supplementing with formula at this stage can be detrimental in that sense as your LO is more quickly able to feed and be full with a bottle, so that time off the breast is time your body doesn't think your LO requires milk and it will adjust supply to that. You can express, however a pump is never as efficient at extracting milk as a baby, so shouldn't be used as a measure of how much milk you're producing. Many women can nurse exclusively for years but are unable to pump even an ounce.
If you want to introduce a bottle of formula, and still keep up supply by pumping while they feed, that negates any benefit of doing it to get some rest. Many women find it easier to co sleep and nurse lying in bed during the night, and for their partners to help out by doing night changes and winding them etc. Remember that the night hours are your most productive for milk supply as well, so not feeding from the breast during those hours can adversely affect your supply.
All that being said, as a mother, you can only do what you feel is best for the health and well being of your baby and whatever you decide to do will be in their best interests.
Just know that you're not alone, and that so many other women are going through, and have gone through the exact same thing. Well done for making it this far!