My son (7 weeks almost) takes a long time to eat as well. He eats for about 40 minutes. He will also go through periods of the day where he wants to eat quite frequently. Please, don't give up! Breastfeeding is such a great thing. My daughter is almost 2 and has been sick only once, not to mention all the other benefits. As your little one gets older, nursing will become easier and shorter.
I would strongly reccomend seeing a Lactation Consultant in person. I wouldn't do it over the phone because you may need some hands-on help. It's so much easier to make an assessment when the consultant can actually see what is going on.
As for inverted nipples, I wish I could remember what these things are called. Nipple guards maybe. It's not a shield because you don't wear it while baby feeds. It's a hard plastic thing you wear between feedings (not attractive, so I wouldn't wear them outside of the house). It's a hard plastic thing that has a hole in one side for you nipple to go into. You put them in your bra and wear them between feedings to help 'encourage' your nipples to move forward. But, your nipples change shape as baby eats. I have flat nipples unless they are stimulated (sexual arrousal, cold temperatures and baby nursing). Then, they become rather large. So, this may not be as big of a problem as you are thinking. Again, see a Lactation Consultant.
Keep up the good work!
God bless,
A.