You made an honest mistake. It's OK, it happens. I would recommend calling the billing department of the doctor/hospital and explaining the situation. They might not believe you, but if you're polite and honest about working with them to rectify the situation, they may be willing to pull the bill from collections and work with you on a long-term payment plan. Once that communication has been established, send a notification to the collection agency, in writing, stating that you have started working with the doctor/hospital on arrangements and that they should contact them for further details. The goal is to get yourself back on track with communication with the billing party.
You should also contact the insurance company and have them review the bill. Sometimes insurance companies receive bills that are coded or submitted incorrectly. Find out exactly why they're not covering anything and see if there is a path to getting the bill reevaluated for coverage. This may entail speaking with the billing department of the doctor/hospital and having them resubmit. The part that can be confusing and is different dependent on your coverage is the fact that the bill was addressed to your baby. Some insurance companies don't recognize the baby as an insurable individual until up to 30 days after birth, meaning all bills would be applied to the mother's coverage (deductibles, out of pocket, etc.) Other insurance companies recognize the baby from day 1 and that baby has their own deductible, out of pocket, etc. You may also be able to have the billing department resubmit as a bill under the mother rather than under the baby. It depends on how things are set up and the contracts they have negotiated with the insurance company.
Communication is your friend right now. Getting as much in writing as possible is also going to be helpful. If the billing department agrees to have the bill removed from collections so you can work with them, get something in writing. Any communication with the collection agency should be in writing.
There are a few other questions on this site that address disputing bills that have already gone to collections, so it may be worth searching for things like "debt collection" or "hospital bill" and reading through them for additional information.