Y is around 100. I tried digging down to 64 but could not find an opening. Since I don't have tnt, I used a bed to create an explosion, but I still did not find an opening. Also tried making another nether portal, but it brought me to the same place.
Yeah, just keep digging, also try listening for mob sounds or fire crackling, that might point to an external area. You could also try turning on Minecraft subtitles as i believe they are range limited, i.e if you are in range of something a subtitle will pop up, so may give you pointers.
This is what happens when you create a "blind" portal--that is, a portal you go through that has no active portal already placed at the equivalent spot in the other dimension. For a first-time entry (in this case, the first person ever to go to the nether in this world), you cannot avoid travelling through a blind portal, but for all other times despite how inconvenient it might be you can set up the portal in the overworld then go to the nether through your existing portal, travel to the spot your new portal would land, and build the nether-side portal at the correct spot.
What is the correct spot? Glad you asked! The correct spot is determined by your player-position coordinates based on where you stepped into the portal. Take the x and z values and divide each by 8 (when travelling into the Nether) or multiply each by 8 (when travelling to the Overworld). These are the destination coordinates where you should build the portal on the other side, and if you do this correctly then the game will never mess up your portal location ever.
Aha! But sometimes when I verify the coordinates and build the portal I still end up having new portals created and ending up somewhere I shouldn't! What gives?! One part of this is just the math. For multiple-of-8 origin coordinates, the math is extremely easy--you divide or multiply by 8 and you only get one number as an answer (ie, 800 / 8 = 100). However, because portals (the purple swirly parts) are a minimum of 2 blocks wide, the conversion isn't quite so clear for the other blocks. Technically I think the game discards the .something, but it does demonstrate the issue since rounding exists. The second part has to do with how destination portals are created when the player doesn't build them themselves. Because the game is only using a single point of reference (player position), the destination portal can be freely oriented in any direction...which means that other than this single block the portals aren't actually aligned to each other...your overworld portal might travel in a north-->south line (ie, z=800 being the spot you entered the nether from, and then the portal is built on z=799 and the other frame being on z=798) but the portal in the nether might be oriented on the x-axis instead (ie, x=100, x=101, and the frame at x=102). This isn't too much of a problem for any specific portal pair like this, it's more that it impacts nearby portals that have landed at the edges of the detection range. If the portal-detection range is 256 blocks in the nether when you entered from x=800, entering from x=801 could actually mean your nether-side portal is no longer within range even though you only stepped one block over in the overworld (ie, it's now 257 blocks away, outside of detection range).