Our situation was not with a newborn but I can certainly relate! My L/O had not seen or held his son since he was 1 1/2 yrs old (he's 5 now), had no contact with him at all bcuz of the mom, no one in the family did. I reached out to the child's mom and after 2 months finally heard back from her. We talked and with MUCH reluctance she agreed to let me take him to see his dad. That same night I surprised him with a call with his son, when he came on the line he expected it to be me but instead he heard his son's voice...he was in TEARS!!! Now this is a strong man in a place where tears are assumed to make you a weak person but he simply could not control himself, that was the BEST 30 minute call of his life!!! He said what made him break down was not only the fact that he was able to talk to his son, but that his son was talking in full sentences and was such a big boy now, the last time he was with him his son was just putting a few words together, half the time making no sense...lol.
On Dec 27 I took his son to see him for the 1st time in 3 1/2 yrs, he had tears in his eyes when he saw his son, his baby boy was his focus thru the whole visit! His son sat on his lap thru the entire visit and he was all smiles, would not let him go at all!!
Based on my experience I can tell you that it will be such a rewarding & emotional time for you all, a great bonding time that will stay with you always. Be prepared for tears, smiles, happiness...ALL of that!! Congrats on the birth of your son, have a great time at your visit and be sure to let us know how it went!!!
And make sure you read Sheridan's rules on what you can bring in with a baby, call the prison to verify ahead of time if you still have questions. I know at Logan they make you change the child's diaper in front of them and then you can take (I believe) up to 2 more diapers in with you, a bottle and (I believe) baby wipes. The IDOC site should tell you, it would be in Sheridan';s visiting guidelines.
BEST OF LUCK< ENJOY!!!!