While I will not talk you out of taking the rifle to a gunsmith, after all safety first, you're not the first to have done it and will not be the last. I've known a lot of people that have done that and not caused damage to their rifle. Visually inspect the barrel and stock for anything that looks out ofquestion. Then put a very tight cleaning patch on a jag and slowly push the patch down the barrel. If you feel the patch suddenly get loose or more much faster and easier, it could be a bulge in the barrel.
If this is an inline it is easy to visually inspect the barrel. If it's a traditional rifle take a .44 caliber empty brass casing, and with brass cleaner, clean the empty casing to a high shine. Then tape the neck of the casing with masking or scotch tape so it does not scratch anything. Drop it down the barrel, it will come right back out by just tipping the gun over. Now with a flashlight you can shine to the side of the barrel and the light will reflect off the casing and allow you to visually inspect the barrel. Its cheaper then a bore light.
The way to avoid doing that and other loading mistakes in the future is, do not allow distractions when you load and shoot your rifle, and second, make a habit of always visually spotting the ramrod before you shoot. I have a friend that will tell his ramrod before he shoots, " are you ready?" While this sounds strange, what he's doing is mentally and visuallychecking the rifle one last time before he shoots.
By the way, how well did the ramrod shoot?

Another person I know did the same thing you did the first time out with his rifle. Now we call him from time to time and tell him Cabela's is having a year end close out on ramrods and it might be a good time to stock up. We still laugh about that. Just glad no one got hurt or worse.