I have just started getting interested in anti-diabetic agents/diabetes medications for research reasons, and regarding possible personal use down the line, and trulicity/dulaglutide was on my list, as I think my glucagon response is screwed up, and dulaglutide is an intervention for this aspect of T2D.
I mention these things below if your side effects do not subside, so you can explore other ways to 'attack' those things that are making you a CVD risk (which reads like is the main reason for your prescription?). If you are rolling your eyes at this (because the old 'diet and exercise' thing IS the number one way to deal with lowering CVD risk, and T2D complications risks) - please forgive me! Just thought I would throw it in here for good measure.
Dulaglutide/trulicity gets prescribed if your medical team, it seems to me, consider you a CVD/heart attack/stroke risk, as this is part of the T2D 'complications' profile as we know. You might have more CVD event risk factors than just high cholesterol? If your side effects continue along the line you are now experiencing (you poor thing! egads!) - this could be an avenue to explore more fully with your medical team/GP, because there are lots of ways to tackle the CVD risk beast. (and changing the drug/s you are taking could be one of them for sure).
Nowadays the whole heart health picture, thank goodness (I too have high LDL cholesterol, and have close family members who do) includes size of LDL particles - rather easily assessed via your triglycerides and HDL ratio, which points to CVD risk to a greater extent, as does your triglyceride level generally. (I am pleased for this, otherwise my life insurance premiums would be way higher!) Any CVD risk self-assessor online includes these readings from your blood lipid tests - it may be well worth it for you to have a look.
High weight too is part of the trulicity referal package, and is a CVD risk factor in itself, even without the T2D, unfortunately - to do with sick fat cells, as far as I understand. I absolutely understand that 'weight loss' is much easier said than done! But that might be part of why your doc/medical team prescribed you trulicity in the first place.
(My tip to all is find out the generic term for the drug for googling, rather than a brand name - the generic name gives you the info for doctors and medical/pharmacological bodies so you get more detailed information, but yes - use both your local brand and the generic name when googling for a fuller profile.)
Here is a fuller list of trulicity's side effects, from a NZ site for medical professionals dispensing medicines, called New Zealand Forumulary
"appetite decreased, nausea, vomiting, gastrointestinal pain, diarrhoea, burping, dyspepsia, constipation, atrioventricular block, sinus tachycardia, atrial fibrillation, fatigue, with concomitant insulin or sulphonylurea increased risk of hypoglycaemia; less commonly injection site reactions (rash, erythema); rarely hypersensitivity reactions (including urticaria, anaphylaxis, and angioedema); also reported acute pancreatitis (permanently discontinue)"