Definitely freezer for 6 months or longer storage. Fridge can last many weeks but 6 months might be pushing it. Hard to say. For long-term storage it’s important to dry the pollen after collecting it. You screen out all the flower parts etc and then when you put it in vials like you have there … you place the vials in flat jam jar that is packed with packets of desiccant.
Jam your pollen vials in there with lid popped open. Put lid on the jar and at room-temp let it sit there for 24 hours. After that close the lid on the vials and place the jar inside a tub or similar (thermos is great) and into the freezer. In your case you don’t need to dry the pollen you already have so you can just store it with the desiccant packets in the freezer.
It all depends on your technique and conditions. This podcast about pollen was helpful.
