Short answer: depends.
Employers don't really like giving raises. Especially that you're new in the company and you agreed upon given terms, you could have renegotiate or ask for more back then. There's also the case that it might negatively mark you in your boss memory. Think about a scenario where you're the CEO of a company and someone who just started working ask you for raise and says that others are paying more. You need to ask yourself if this job is worth doing for less money than the other perhaps you like it more and as you said you feel good there. Depending on your contract you might just ask next potential employer to ask until your current contract expire if you're in position to do so. This might give you some time to think. But by doing so you might be perceived as unreliable and don't gain enough trust.
Don't do anything sudden and think through every possibility. Chances are you won't be able to go back to the company you're leaving.
From personal experience I know how hard this decision might be on you right now. Because if you won't take job with better pay you'll have regrets which will affect your work at current company. If you take the job and it's worse you'll regret not staying because you might find that bigger pay isn't worth the stress.
Good luck