This does sound like the clutch is not fully releasing. Start by flushing and bleeding the clutch hydraulic fluid.
Something else that helps with the first few shifts in the morning is to start the engine with the trans in neutral, let the clutch out after the engine is running to allow the fluid to splash around in the trans and get into places it would not for a while. Some even suggest gently tapping the throttle twice to bring the cold idle up to about 2000 RPM. I usually start the engine, ldt the clutch out, strap on the seat belt, depress the clutch, shift into 1st, then drive away. That few seconds in Neutral before engaging the trans helps with shifting into 1st and also helps with the first 1 to 2 shift. Otherwise, the trans can be a bit balky when the weather is close to freezing or lower.
