I got a really weird headache (for me) 5 days after the AZ jab. It was a very mild headache, but got quite a bit worse when I lay down. Painkillers didn't make it go away, when they usually do for me. Under normal circumstances I would have just carried on, but given the timing, and what the nurse said at the jab, I phoned my GP, and she sent me to A and E immediately! They didn't let me go until they'd done a blood test (for platelets) and a head scan, with really, really frequent observation for BP/ reactions/ oxygen and so on throughout. (The whole thing felt like absolute overkill to me given the mildness of the headache and other things happening in A and E at the time, but all the staff confirmed I'd done exactly the right thing...) I was fine - it was just a headache - albeit a really weird and unfortunately timed one!
I'm not particularly anxious about my health at all, and wasn't worried about clots happening beforehand, but I must just have been hyper-aware that this headache didn't seem normal to me, and it was made really clear to me what to look out for and what to do in that case. I assumed it would be severe, too, but the "lying down" thing alone was sufficient for the NHS to take it seriously and start on their protocol.
This anecdote may not help your situation at all, but my experience was that the NHS do take the risk very seriously, and act very quickly to investigate it, and treat if needed. And I'm pretty lax about noticing when something probably should be seen by a GP - but in this case, it wasn't something that I missed, purely because of the emphasis put on the symptoms.