libralady we don't usually recommend nipple shields because they can cause more problems than they solve but they certainly have a place and can help some Mums. First you fo not need the nipple pointing out to successfully breastfeed it is the darker area that is going in not just the nipple it's self but having the nipple there as a guide line is a helpful marker as to where you are heading when you first start. I have seen Mums with inverted nipples successfully breastfeed so it can happen please take heart if it does not you will have done your best and this dear child will be just as fantastic and wonderful as your previous child, at the need of the day as long as you and they are well how you feed them does not matter.
Not sure what you have tried but I will go through what we would normally recommend.
Skin to skin - sounds odd but if when he is just starting to look a little interested (no good if at screaming stage) strip him off down to nappy, get yourself somewhere comfy take off your bra and pop him down your front right next to your skin. This helps in 2 ways first it is good to increase your milk supply second it encourages the baby to naturally open their mouth as wide as they can. This will give you the best chance of getting a good fix.
Tweak your nipples before you feed. - It does depend on how inverted your nipples are but this can sometimes along with the cold bring the nipple out but I know it does not always work. If you have a hand pump this can also help to pull out the nipple just means you are tied to feeding for that much longer.
Can you cope with your nipple shields in your bra all the time? You may be able to encourage your nipples out by keeping them in all the time and the gentle pressure sometimes brings them out. Wish I had known you had a problem before would recommend anyone with inverted nipples did this for the last 3-4 months of pregnancy if they want to breastfeed but a bit late now it can help afterwards too but you still have the stress of getting things started. It's sad Midwives no longer check breasts it used to be something that could be picked up and helped before you got to the desperate Mum trying to feed stage
There may also be an easier way of getting milk down little one rather than a syringe Has any one mentioned cup feeding (strange thing to talk about with a baby I know) it's not as effective with a term baby and can be messy but it is easier to get a reasonable volume down than with a syringe and very slightly more natural. It is a technique we usually use with pre-termers who are ready to take oral feeds and Mum is not there for that feed. If you have bottles often the cap which covers the teat is the right size and shape if not try an egg cup (sterilise what ever you use)
reasonable youtube video of cup feeding
Other things about cup feeding
www.breastfeeding.asn.au/bfinfo/cupfeeding.html
www.breastfeeding.org/articles/cup.html
www.babyfriendly.org.uk/items/research_detail.asp?item=475