Some tips on breastfeeding:
My 1st kid was in the NICU for a week, so it was also a transition. I urge you to stick with trying though, because later on it is so much easier than having to always bring bottles with you.
First, if you can find a good lactation consultant not attached to the hospital, then do it. Mine was not too expensive, and I saw her many many times until we were doing better.
Now for tips:
The nipple shield can stay on you without falling off if you kind of roll it back a little, then roll it on so some of your nipple is stuck inside. So roll it a little like you're trying to push the nipple part of the shield in a bit, then roll it onto yourself and it should stay.
Don't feel like you have to try without the shield at this point, as that is a transition too, and baby is used to bottle type nipples. Get comfortable with the shield first, then make the transition off of it.
Make sure you are bottle feeding for a breast-fed baby. This means not tipping the bottle all the way up, but only horizontal to the ground so the nipple is just filled with milk. This mimics breastfeeding more because at the breast, the baby has to do work to get milk, but at the bottle, each swallow provides enough suction to get a mouth full of milk without break. This is actually too much for baby most times, so you need to give them a break at the bottle. They have no ability to pause if at each swallow they get another gulp of milk in their mouth. They swallow again so they don't choke. Horizontal bottle and frequent breaks allow them to not gulp. (sorry - a little wordy!)
Lastly, our LC had us work on his suck to make sure it was stronger or breastfeeding. This involved using a tiny tube you taped to your finger and put the end of it in a bottle to finger-feed with. If the bottle was held higher, our son would have to suck stronger to get the milk. We did this several times and I think it helped.
The amounts you mentioned sounded good. Baby might be used to having to do no work to get food, so he will get sleepier and fussier at the breast as he goes through this transition with you. And it's ok. And it's fine to go to the bottle sometimes to avoid frustration. This whole process came with a lot of emotions for me and the LC said take small steps but keep at it. I really encourage you to keep at it! We finally weaned from the nipple shields after a couple months, and it was terrific. They are a pain to wash all the time and have handy all the time. But after those few months, we breastfed for 2 1/2 years.
Hopefully you find a good LC near you! Also, a good breastfeeding resource website is www.kellymom.com. Tons of great information!