No travel agent or holiday company will accept a booking from anyone under 18 unless an adult acts as guarantor. That's because you have to be 18 to enter into a legal contract (which is exactly what a holiday booking is).
Some firms will accept bookings if an adult acts as guarantor but others might not.
The best way to make your travel arrangements is to book independent travel, rather than buying a package. To the best of my knowledge, all airlines permit unaccompanied 16-year-olds to book flights and to travel unaccompanied by an adult. Most online booking services for hotels will also accept the bookings but it would be wise to contact the hotel directly, before committing yourself to a booking, to check that you wouldn't be denied accommodation upon arrival.
A further consideration is the immigration rules of the countries which you might be considering travelling to. You'll have no problem with most countries (including Spain and the Canary Islands) but you should be aware that Portugal doesn't permit unaccompanied under-18s to enter unless there is an adult who will take responsibility for their stay.
Chris