Is it normal to submit a paper just after the acceptance of another?
Yes.
It is probably the best time to do so. The editors won't have time to forget who you are, or to forget that you did work good enough for them to accept in the past.
Journal editors at all but the very best regarded journals are constantly scrambling to find papers to publish that meet their standards so that they can get out each new issue. Often they get a fair number of submissions, but a lot of the submissions are awful, and if they have no other choice, they will hold their noses and publish them anyway. But that isn't their preference.
Submitting another up to snuff paper is something that most journal editors would see as a blessing and a lucky break. Usually, this would be appreciated.
If a journal has a policy of waiting before publishing another paper from the same author, they'll usually tell you that. And, often, the policy is to wait so as not to publish a paper from the same author in an immediately following volume of the journal. Even if it has such a policy, the journal may be happy to accept your paper but sit on it for a volume or two before publishing it, if you are O.K. with that. Or, the editor considering your submission may tell you that your paper looks good and that you should consider resubmitting it in another six months after their internal waiting period has expired.
The worst case scenario is that your submission is rejected and you submit it somewhere else. Nobody else needs to be told that you were rejected the first time and many fine papers in history were rejected multiple times before ultimately being accepted. Don't overthink it.
