If I haven't prayed for a long time and even done acts forbidden in Islam, but I repented and want to become a better person again, following Islam, do I have to do my Shahada again?
No, if you were born to Muslim parents or if you are a revert having said your shahada in the past, then you don't have to do so because you are already a Muslim. You should only repent and ask Allah for forgiveness and start doing your religious obligations while also compensating for your missed obligations according to the fatwas of the religious scholars you trust and follow.
If the sins done have ruled you out of the territory of Islam, hope not, then reasonably yes, but otherwise you are still a Muslim, hope you are not such but at most a sinful Muslim (Fasiq).
By the way we all repeat Shadah in our everyday Salah, at least 9 times per 24h, similarly it will have no problem if you say that elsewhere ;)
Becoming a Muslim needs that saying with mouth so you can try it this time by saying it with the words coming from also your heart!
As a general rule:
"الأَعمال بالنیات", "the doings are measured by the intentions behind them"
And relax, Allah the most exalted and merciful will never punish you when you intend to yield to His obedience, returning back to the right path.