Also it could be thermal activity
Yeah, I was wondering that from the description, having had it happen to me. (I went around.)
Wha'ever; if you are absolutely certain that you understand what is happening and are in complete control then by all means rescue the landing.
Otherwise a go-around is going to sort it out much more reliably than carrying on, and waiting to see what the aircraft does next, and hoping for the best.
In my case the thermals blew me all over the place. I went around. The second time, the thermals blew me all over the place again. I went around again. The third time I landed on the grass runway, which doesn't suffer from this problem.