I've been to Egypt 3x. The last of which was 8yrs ago, but at that time, you arrive and within the airport is a counter saying something like 'foreign visas'. You line up, pay the fee and they stamp your passport.
Driving in Egpyt can be erratic, fast and scary my UK standards. Depending on the time of year, it can be incredibly hot too. I'm unsure about roadside services and the availability of toilets, so keep those points in mind before agreeing to a 3hr drive! Is it a bog standard taxi, is it an English speaking chaeffeur, will they stop if you need the loo, is it an air condtioned private car or a mini-bus full of others?
Have you never been abroad, or always used a travel agent to book, when you say you've never booked a flight abroad?
Have you checked the cost to have this op within Europe? If you post what op it is, people might be able to give you a recommendation.
As mentioned, I'd especially check your travel insurance and any clauses. Will you be covered on the NHS for any corrective procedures, revisions or infections? (I assume so, but I'd read otherwise in come cases).
Check if you need a 'fit to fly' certificate before you can return to the UK
Will the surgeon in Egypt refer you to a surgeon in the UK for follow up/referral?
I worked in A&E years ago. We had a women turn up to A&E having returned from surgey in Egypt. She had drains still attached and said she'd had gastic banding surgery. She had no documention of what she'd had done, now idea how long the drains had been in nor her the Egyptian Dr referred her or spoken to any Dr in the UK for follow up. We obvioulsy couldnt just 'pull out' the drains at her request!
Is anyone going with you? I'd seriously consider against having surgery abroad, even more so during a pandemic. It might end up costing you alot more than you expect.