Yes, been there: vertigo.

It is probably caused (in your case) by a temporary loss of sufficient oxygen. Standing takes effort, certainly in comparison with sitting.

Another possibility would be (slight) hyperventilation. It's subconscious and probably due to some proprioceptive changes which make you react to them.

In both cases you need to give your body/mind some time to adjust.

Lastly (for me), vitamin deficiencies could cause it. Induced by the lamotrigine increase or not.
If I had to guess: try D; is often deficient, certainly in us.

For me it went away after a while. Hope you feel better soon.

Also, still make sure to check there is no rash.