First of all, might I suggest that you get a letter from your doctor giving details of what you are carrying and for what medical condition. The letter should also insist on the need to keep the medication at the temperature range you state.
Secondly, take only the sharps you need for the period of the journey in your handbaggage, with the letter from the doc to back up the reason you need them. Put the sharps for the rest of your holiday in the holdbaggage.
You should also contact Manchester Airport and discuss with security there how best to take these items through their control points. If the worst comes to the worst at Antalya, you may need to get 'supplies' from a spare UK prescription at Manchester Airport's pharmacy if it's open at the time you return home IF Antalya security takes these items off you (assuming the timing interval between security and your return to Manchester falls inside the period for your dosage scheme). Manchester airport's website says there's a Boots at Terminal 1 in Arrivals. See
http://www.manchesterairport.co.uk/manweb.nsf/Content/RETAILERBootstheChemist for more information.
Airline crews have specific bins for sharps disposal on board, but they will probably ask you to put them in the bin so they don't have to touch them. Check their website and also ask about what they can do to help you ... sharps disposal and use of fridge ... well in advance of travel.
I am more concerned with the way of keeping your meds cold not only during the journey but also during your holiday. First of all, you should think of the time you will need to pass through the airport and also the transfer time to your accommodation (depends also on where it is on the transfer route). Some transfer drivers have a fridge or cool box to try to make a small profit by selling water and beer to arriving passengers .... so if so, you might be able to use this. Antalya at midnight in summer is still pretty hot!
However, the temperature level for your medication is pretty specific. I'm not even sure that a fridge in your accommodation would be able to ensure a constant temperature, especially if there's the unlikely but never to be discounted possibility of power cuts. (Check if your hotel has a back up generator!)
Ask your doctor if he can write you out (in very clear handwriting or typed on HEADED notepaper) an emergency prescription for sufficient medication to cover you for your stay and homeward flight, fully signed and stamped by him!!! This might be sufficient if you need to replace your stock ... but you may not be able simply to go to a pharmacy and ask for it to be filled (with payment of course) and you might need to have to take it to a local doctor for it to be replaced by a valid Turkish prescription (again you'd need to pay ... Turkey is not covered in the EHIC reciprocal scheme). You might also ask him to do this for your sharps.
Is there no way that your medication could be provided in another form ... a dried dose that can be made up with sterile water and then injected? Something else to ask and I'm aware that this can be very fiddly.
If you are referring to diabetic medication, I am sure that either the same medicine (at the same dose) or something very similar will be available in country for Turkish diabetics. The problem is how to get hold of it! You might find that
http://www.expatforum.com/expats/turkey-expat-forum-expats-living-turkey/ might help ... you'll have to join and ask a question if there's no information already existing. What about posting on the Turkey forum here on HT also, or even on Trip Advisor. You can't be the only person who's ever had to sort out this problem!
You might also find a starting point for suggestions here
http://www.childrenwithdiabetes.com/d_06_800.htm This might be just what you are looking for
http://friouk.com/ because you can start it working at any time!
Good luck with your research and have a great holiday.
