With BMI > 30 you should be eligible.
It absolutely makes sense to talk to some people about your diverticulitis, GLP1s can cause constipation, diarrhoea, gut slow down. At least to find out what you should look out for and how to manage in relation to your diverticulitis.
I would discuss with whoever knows your diverticulitis history best for their advice.
Then I would try a Dr led pharmacy such as Swift Doctor with experts on Mounjaro/Wegovy and book an online consultation to discuss, focussing on how they would support and monitor you. I think Swift Doctor charge around £30 for a consultation. I think a Dr led pharmacy who specialise in weight loss are likely to be more informed than a local pharmacy who is simply selling.
Scan the internet for information on diverticulitis and GLP1s.
Use forums/chatgpt - mumsnet, facebook, reddit for any information/anecdotal stories. More for confidence if others have done it without significant issues than actual evidence.
Then consider your options.
Also, the pens are designed for self injection, it is a bit scary the first few times, but the needle is tiny (4-6mm) and mostly painless. Once you manage the first one it is fairly easy.