You should not have to pay your doctor to complete your certs. A gp normally receives a per certificate payment for filling these out. AFAIK this is €13.50 per cert.
Jobseekers benefit means that you are capable of working and actively seeking work. If you have injured your hand then you more than likely are not able to do this. You risk having your payments stopped if you're claiming the incorrect benefit.
The con of being on illness benefit is that it works in arrears, rather than advance. Jobseekers benefit is paid in advance. When you hand in your first certificate be sure to check with your local officer how many weeks you should continue to claim your jobseekers for.
Payments are made directly to your bank account providing you continue to hand in your certs on time. This eliminates the need to collect from your local post office and/or signing on a regular basis.
If you're on jobseekers benefit have you applied for your medical card?