You need to file a Suit Affecting the Parent Child Relationship (SAPCR). In that suit you will ask for joint managing conservatorship, possession and access, and offer to pay guideline child support.
The standard possession order, which is the one that gives the possessory conservator every other weekend, etc. does not automatically apply to children under the age of 3 so your visitation will be determined by the court. Some courts order a 50:50 possession and access schedule with newborns, many only allow a few hours of visitation at the mom's house.
You should hire a local family law attorney to help you through this. You need to file as soon as you can. For every month the child lives, you are accruing a retroactive child support obligation. Get orders in place, make sure both sides follow them, and you will have more peace in your life.
I'm glad you and your wife were able to work things out.