You are right. Adrenaline does increase Blood Pressure by increasing heart rate.
I have placed a more complex explanation below, that may be of some help to you.
For this explanation I shall use alpha = A and Beta = B.
Vasodilation is the increase in the size of blood vessels and Vasoconstriction is the opposite.
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Adrenaline combines with both A1 and B2 receptors. These receptors are found throughout the body on different blood vessels.
However they have different effects. B2 causes vasodilation whereas A1 causes vasoconstriction.
B2 receptors are largely found in the blood vessels in the heart and skeletal muscle.
Therefore, during sympathetic release, Adrenaline causes vasodilation in blood vessels of the heart and skeletal muscle.
So, Adrenaline has two effects on the heart. It increases the heart rate AND it also causes vasodilation of surrounding blood vessels. This enables more blood to be pumped around the body by the heart.
The second part is that Adrenaline effects organs with A1 receptors like the vessels in the Kidney. This causes vasconstriction in these vessels. Therefore, there is more blood going to other part of the body that need it, such as the skeletal muscles.
If there is a term or part you do not understand then just say.