Its always wonderful to meet new believers - welcome to the family. It is good that you are talking to others about it and also asking questions - knowledge and understanding (tempered by love) are what help us to mature and hold firm in our faith.
The English word baptism comes from the Greek word to wash or make clean. Baptism services, can vary between denominations, but are essentially a service where a person professing their faith in Jesus undergoes an act of washing to show they have been washed clean from their sin and therefore are in a right relationship with God.
Now the bible quite clearly teaches that no human ceremony can actually cleanse people from their sin. It is only the true baptism of receiving the Holy Spirit which can make someone clean. Therefore a baptism service is an outward sign of what we believe God has done inwardly through his Spirit. If a person has not come to trust Jesus and his death on the cross to pay for sin, then a baptism service will not bring someone into a right relationship with God. So a baptism service is not necessary to make someone a Christian.
However a baptism service, if used correctly, is very helpful. During a baptism service what is being done is explained and the person declares that they have put thie faith in Jesus. This public act of expressing that you have become a Christian can be very encouraging step in your christian life and I would recommend it.
With regards to the issue you’re having in your church, this is a delicate issue. In Matthew 28:18-20, Jesus commands the disciples to go out and make disciples of all nations and baptise them in the name of the Father, Son and Holy Spirit. Some denominations have taken this to mean literal baptism, others have taken this to mean the baptism of the Holy Spirit that comes at conversion. Some churches even make it a matter of membership (as in your case). I personally wouldn’t exclude someone from church activities because they are not baptised. But those that do are not necessarily wrong to do so either. Speak to your minister and listen carefully to what he says about baptism. Ask God to enlighten you and give you wisdom about it and then act as you think best.
Hope this is helpful.