a 1944 Cent is what is also called a Shell Casing Cent If it was in better condition it would be worth more than face value Yours is circulated and worn I want to share this webpage with you - http://cointrackers.com/coins/13596/1944-d-wheat-penny/
Any time you find a wheat, it's a good find. Just keep searching, and you'll find better...and older. We averaged one wheat every six rolls.
Your 1955D is a run-of-the-mill Lincoln Cent. But you have a start. Do you collect cents or just save the occasional one that looks different?
It is fun, isn't it. How do you keep them? Do you have an album. Unfortunately for the entire run of Lincoln cents, there are probably only a dozen or so that are worth any moderately significant money. I remember as a kid getting a 55-S in change and thinking it was a big deal.
@Marie S., can you manage a sharp close-up of the D mint mark under the date? There is a method to my madness, lol; you might have one of these little things: http://www.coppercoins.com/diesearch.php. Or look closely at your D and see if it looks like any of these. Your pictures are blurry at the high-zoom level, but I think I see one of these.