You can choose to have the sacrament of marriage if you want to. By that I mean the marriage ceremony. We did that when we were received into the church by baptism and confirmation.
Convalidation is what people mean when they say getting a marriage “blessed” but convalidation is actually the form of making something that was invalid, valid. As in the case when Catholics marry outside the Church without a dispensation.
Your marriage is a valid natural marriage and does not need to convalidated. If you want, you can choose to have the sacrament of marriage after you are baptized but you can receive the eucharist after your baptism either way.
Confirm with your priest what your options are. We had ours in front of the altar at our church.