I too own in Horizonte Playa Flamenca since 2004, maybe we have met in a bar somewhere!
Anyway, yes, you can pay your own taxes and save a lot of money in lawyers fees.
You can pay online, there is a process to go through though.
Firstly you would need to gain a certificate for the computer you will use to pay your online taxes.
This can be applied for online, but you will have to visit the tax office in Orihuella City in person, to have the certificate validated before you can make your 1st online payment.
alternatively, you can pay them in person at your local bank annually when you visit for your holidays
Check my website out for further info
Hope this helps