When taking Saxenda my heart is racing a bit. I buy privately. If I go to my GP she will just...

Cardiovascular
Chronic Weight Management:

Very common (10% or more): Increases in mean resting heart rate

Common (1% to 10%): Hypotension

Uncommon (0.1% to 1%): Cardiac conduction disorder, tachycardia

Type 2 Diabetes Mellitus:

Common (1% to 10%): Increased heart rate[Ref]

Chronic Weight Management:

Cardiac conduction disorders were reported as first degree atrioventricular block, right bundle branch block, or left bundle branch block.

Increases in mean resting heart rate of 2 to 3 beats per minute (bpm) were observed in clinical trials. Increases of 10 and 20 bpm at 2 consecutive visits were 34% and 5% in liraglutide-treated patients versus 19% and 2% in the placebo group, respectively. Resting heart rate exceeding 100 bpm was recorded for 6% of liraglutide-treated patients versus 4% of placebo patients. Tachycardia was reported in 0.6% of liraglutide-treated patients compared with 0.1% of placebo patients. Monitoring heart rate over 24-hours found that liraglutide treatment was associated with a 4 to 9 bpm higher heart rate than placebo. The clinical significance of this is unknown.[Ref]

Source: https://www.drugs.com/sfx/saxenda-side-effects.html