I am sympathetic to your problem since I had (and have) it, too, as a non-native English speaker.
Spellcheckers are easy to use and reliable, so use them everywhere you can. Even as I am typing this answer I get a squiggly line below every incorrect word.
Grammar is completely different though. As far as I know there is no easy way to check it in an automated way. Some software tools are listed in this thread on tex.se, but even an intermediate English speaker would find most of them disappointing; they do catch some missing 's', but with so many false positives and negatives that it's hardly worth the effort to go through the results.
My suggestions would be: either (1) find some English exchange student willing to proofread at much cheaper rates, or (2) ignore the issue; it's not so important. I am not a native speaker myself, so I am not in the best position to judge, but your English looks clear enough to me. As long as the paper is understandable to the referees, it shouldn't be a problem if there are occasional grammar errors. After acceptance, the journal's copy editors should make a full grammar check and proofread for you for free as part of the publication process. By going through their correction you can identify the typical mistakes in your English prose and try to improve when writing the next paper.
I work in mathematics; if you are in the liberal arts the situation could be very different though.