Yes, the Holy Spirit is God.
The Holy Spirit is spoken of throughout the Bible as God’s Spirit. By the time we get to the New Testament, it is clear that the Holy Spirit is seen as God. In Acts 5:3-4, Peter says “Ananias, why has Satan filled your heart to lie to the Holy Spirit and to keep back for your self part of the proceeds of the land? ... You have not lied to men but to God.” The Holy Spirit and God are seen as one.
In other places in the Bible though, we can see that they are not the same. That is, that Jesus, God the Father, and the Holy Spirit are all God, but are all distinct. In 2 Corinthians 13:14, Paul closes his letter with “The grace of the Lord Jesus Christ, and the love of God and the fellowship of the Holy Spirit be with you all.” This is a statement where the three identities within the trinity that is God are all stated. So they are distinct from each other, but also unified and equally God. We can also look to Jesus, who commands his disciples to “make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.” (Matthew 28:19) This again shows that each of the three is God - they are equal, they are unified, but they are distinct.
There is lots more that you can think about with regards to the Holy Spirit. In John 14, Jesus talks about the Holy Spirit comig after him. This may be a good place to start if you want to do some investigating of your own. Good luck!