I was taught that souls go straight to heaven or hell, but I feel that the souls of my loved ones are still around me. Could it be that souls stay on earth until that final judgment?

Yes, to be absent from the body is to be present with the Lord. For the Believer, immediately upon death you are in Heaven.

Since we will be “like the angels” I have no doubt that our loved ones in Heaven can see us here on earth, and probably are in front of the throne continuing to pray and intercede on behalf of their loved ones still here. That is probably the presence you feel, and the Bible does say we each of us have angels round about us ministering and protecting us. No doubt some of those angels come into close contact with our loved ones in Heaven and radiate some of that love back to us on a daily basis.