Yes a freezer bag will be ok, Aldi, Ikea, ASDA whoever just make sure its 20x20 with a ziplock or press seal at the top.
You can buy 100ml bottles if you need to to fill up with liquid items, just decant and you know its correct. You can also buy many items specifically for had baggage that does not contain more than 100mls
Be careful with hand baggage size, manufactures say fits cabin baggage requirements, but who's???? There are so many
55cms height by 40cms width by 24cms depth is what Air Lingus allowance is, make sure you measure the wheels to the very top. They can take your case from you and put it in the hold if its to big.
For this reason I always have a plastic carrier in the pocket to put any valuables/medication, glasses, reading material and so on in, if for what ever reason the bag needs to go in the hold.
I travel a lot and have a routine for hand luggage!