Any parent can be the victim of assault. The Local Authority would be prevented by the family court from removing your child because you have been attacked and took what appeared to be the appropriate action to protect yourself and your baby. That is straightforward.
You have freely admitted lying to the police about what appears to be a serious offence, however, and a baby can experience significant harm from exposure to domestic abuse. Apart from the obvious risk of being physically hurt, your baby (whose age I do not know) can come to associate good things - a warm bed, a loving parent, feeding time, home - with aggression and violence. If they are too young to have speech and understand words, they will not be able to explain that this is not right, or to understand you explaining it.
Your baby could grow up thinking shouting and fighting are the ways to settle arguments, or that violence is normal and acceptable. They can take on the personalities they see and hear: screaming, shouting, hitting. They can fear going to bed if that is when the shouting starts. They can become a low priority as one parent tries to avoid upsetting the other, sometimes spending hours alone so the parents can be together and do parent things.
Police have attended an incident where a baby might be affected, even if the baby was not actually present at the time: domestic abuse can be a one-off incident, but not always. Your baby is at risk, so the police will inform social services.
Social workers are legally prevented from interfering where there is no risk. If there has been an incident but it has been dealt with properly and they can be sure your baby will be safe in the future, they must leave you in peace unless you ask them not to.
What you describe is a partner with a history of violence, an incident that raises concerns about your baby's safety, and your willingness to lie when it suits you. More worrying for me is a suggestion that you were not 'the victim', which makes me wonder what you might have done to your partner that was worse than the GBH that the police think they can prove.
Nobody can consider a baby safe in a home where significant domestic abuse either happens or is used as a tool in disagreements - "Do what I star or I'm telling the police you hit me". You should expect to be contacted by a social worker. You are already on shaky ground a second as you have lied, either to claim there was violence or to claim there wasn't.
In my experience, however, there are very few times that the future is set in concrete. The best thing you both can do is to tell the truth to police and to social workers, and to work together on a way forward. It is likely this will feel pretty carp to start with, but the Local Authority really do not want your baby, and genuinely believe they should live in their own family. You, nobody else, have painted yourself into a corner. You can fight against those who want your baby to be safe and likely lose them, or you can recognise you have done wrong (you, your partner, or both of you) and work with people you might currently see as 'the enemy' but who would prefer you were all on the side of keeping Baby safe.
Whatever else you do, avoid getting into forums and discussion groups that exist to attack child protection services. People who have already messed up and lost children,will use you to feel better about themselves. "See how unfair it is? Now they've taken Sallyann87's baby!"
You face a struggle, but there are people who want your baby to be safe in your care. I really hope you are one of them