J.T.
My boy was 20lbs in 4 months, and I had the same problem that he could not sit up yet but I needed to put him in the grocery cart.
Go out and buy another infant car seat. There is one at BabiesRUs that goes to 22lbs, 29in. That took me till he could sit up, which was a little late since he was so big-- a lot to hold up!
Resell your other seat on Craig's list. Since you've only used it 11 weeks, you'll get top dollar.
The carts with the carriers in them just creeped me out, and I'm not a germaphobe.
btw... when you do buy a car seat, get the largest one you can find, because they will grow out of it before they are ready for a booster seat. I've got a Safe Guard and feel it's the best investment I've made for my kids. They're pricey--$400, but I spent that much on a radar detector (or my husband's golf driver). The are SUPER easy and quick to install and one of my cars doesn't even have latch. They are front facing only. You buy online. I was really happy with Albee Baby's service, and free shipping.
Britax Boulevard is another choice if you need rear and front facing, but it really sucks as a rear facing seat. Hard to get in to, hard to adjust, but the best side impact seat I could find. $250 at BRU. Good luck!!