Could definitely be allergy-related. I find that my allergies feel worst when I first wake up, even if I take medication for it. I believe this is because my sinuses tend to drain some at night, thus bothering my throat and then I often get the headache too. I haven't really figured out a cure for this (unfortunately!). I thought that maybe my older mattress can be contributing to the troubles (more dust mites), but I just bought a new bed and entire bedroom furniture set, including special mattress cover to help with allergies, bamboo shoots, and hypo-allergenic pillows. I feel about the same (although my bed is much more comfortable!).
Let us know if you are able to find something that helps you! I found that sinus rinses DO help me, but then my throat feels a bit worse. I also use a bath soak (but while I shower, I just let the water collect some) meant for sinuses. It smells kind of like Vicks Vapo Rub and is very refreshing and helps before going to bed.