1) Human growth hormone (HGH) shots, meals and glucose and insulin spikes.
HGH shots increase blood glucose and therefore insulin, both of which can be further increased by having meals shortly before or after the shots.
There is some evidence that glucose spikes (International Journal of Clinical Practice, 2002 ; Clinical Therapeutics, 2005) and insulin spikes (Hypertension, 1985) after meals may be a risk factor for atherosclerosis. Theoretically, this could mean that having meals close to HGH shots could increase the risk of atherosclerosis, but there seems to be no direct evidence from the studies.
To prevent high blood glucose spikes after meals one can try to avoid foods with quickly absorbable carbohydrates, such as sugar (sweets and sweetened beverages) and plain starch (white bread, pasta and rice, potatoes, cornflakes, instant oats) (Harvard.edu).
It may also be a good idea to get tested for Hb1ac - increased values are a sign of chronically elevated blood glucose.
2) Human Growth Hormone and Diabetes
Treatment with human growth hormone can increase insulin resistance, but can increase the risk for diabetes type 2 mainly in individuals with other predisposing factors, such as obesity and family history of diabetes.
Study 1) Human growth hormone (HGH) replacement therapy at a low-dose (9.6 μg/kg body weight/day) can increase insulin resistance after 1 week and 6 months of therapy (JCEM, 2003).
Study 2) The effect of 3 months of recombinant human growth hormone (GH) therapy on insulin and glucose-mediated glucose disposal and insulin secretion in GH-deficient adults (JCEM, 1994):
We conclude that short term low dose rhGH treatment of GH-deficient
adults induces a temporary state of mild glucose intolerance,
hyperinsulinemia, insulin resistance, and raised NEFA levels at 1
week. By 3 months, these metabolic disturbances had returned to
baseline for a persisting modest hyperinsulinemia.
Study 3) Incidence of Diabetes Mellitus and Evolution of Glucose Parameters in Growth Hormone–Deficient Subjects During Growth Hormone Replacement Therapy (Diabetes Care, 2012):
Diabetes incidence appears to be increased in GH-deficient patients
receiving GHRT [growth hormone replacement therapy] and exhibiting an adverse risk profile at baseline.
Study 4) Incidence of diabetes mellitus and impaired glucose tolerance in children and adolescents receiving growth-hormone treatment (Lancet, 2000):
We postulate that the higher than expected incidence of type 2
diabetes mellitus with GH treatment may be an acceleration of the
disorder in predisposed individuals.
Conclusion: Even if meals near HGH shots increase blood glucose and insulin levels, there is no direct evidence from studies that they actually increase the incidence of diabetes or atherosclerosis.