Is there a way to add streets by manually entering latitude and longitude coordinates?
Yes, but if these have come from GPS, they are likely to have position errors that need smoothing out, and if they have come form another source, you may need to check that source is permitted and follow the rules for discussing mechanical imports.
JOSM allows you to add nodes with explicit coordinates, and you can also hand construct a .osm file quite easily.
Hi
Welcome to OSM and the forum.
Please tell us which editor you use.
Assuming you are using JOSM, check this posting: https://help.openstreetmap.org/questions/864/how-to-add-node-with-exact-coordinates-in-josm
If you have a whole GPX-File you can load the file in JOSM and convert it to a data-layer.