Does it look bad to ring HR and ask could they consider me for that
position even though I accepted an offer for another?
Updated based on additional input from the OP
It depends greatly on the company and the differences in the positions. But yes, it could look bad. In your case though, I would say the risk in asking is pretty low, so why not ask? The risk of a negative reaction in my experience goes up with the level of the position which you are applying for.
For your consideration, the potential risks and reactions of asking
Don't be surprised if you decide to ask if the company wants you to stay in the position you already accepted.
From another perspective, the company could react more negatively than you may anticipate. The hiring manager may think "Ok, the candidate ( you ) are already prepared to move on from the position they originally offered and you accepted. Does this person really know what they want?"
And finally, the company may just move on from you all together, which I have seen happen in the past.
These are points for your consideration, to assist you with weighing the risk of the inquiry, regardless of how small the risk may be.