I can't say that you have the correct ammo for the gun from here but it sounds like you have general gun familiarity. I'm not sure about your 9mm but if you ever fire a squib (a weak round - say, primer, no powder) that does not make it out of the barrel - you will be amazed at how tight the tolerances are. A wood dowel works best (stiff but no sharp edges) BUT you literally have to pound the bullet out of the barrel.
Rifles and pistols are different birds. Vastly different pressures etc. The 9mm may have fluting / wear at the end of the barrel.
My advise - for peace of mind stop in at the shop where you bought the gun and take the ammo with you (bring it in safely, cased, bolt open, ammo separate) and ask a knowledgeable person (gunsmith, rifle shooter behind counter) the same question with an answer to YOUR satisfaction. Let them handle the gun and ammo.
I'm guessing that it's all good. You are right to stay safe in new territory!!
Get a good second opinion and happy shooting!