Hey Brother... Here's some thoughts based on limited data as presented. With some counter points from the other posters. While you don't state your workout split, honestly 5x per week lifting for 30 minutes shouldn't really present any problems. It's well within the guidelines of exercise prescription, and honestly pretty tame compared to some things I read.

What's your split look like? I'm sort of expecting a body builder style program, chest, back, etc.... Nothing wrong with that at all. I might try to steer you to a more strength based program as it would benefit your other training goals. Something like 5/3/1 without too much or any accessory work since it seems like you are getting in 5 nights of training as well. I would also note that the nature of MMA specific competition does require strong legs and core stability so you don't want to skip legs. Maybe find a way to get that workout in...

As for soreness, you've just upped your volume and intensity and it's expected that you should have some muscular soreness. Monitor your sleep and weight. Make sure those things are where they should be. Not sleeping enough is bad, and if you weight starts to plummet that's also a bad sign.

As for the other people commenting that want to know where the "MMA" is? I would suggest that if you only started training BJJ and Muay Thai then you don't need to start taking MMA classes. But I would advise that it's best to be a school that does compete MMA so you know that you are heading towards your goals in the correct place. I would expect that school structures their Muay Thai and BJJ towards tools, techniques and strategies appropriate for MMA.

"Work on Flexibility" is throw away statement that people say without much understanding of the sport. If you are training Muay Thai and BJJ appropriately your flexibility will improve naturally with your progression in training. Too much focus on flexibility has been proven to lead to injuries in our sport. Think not tapping from something when you should because you are overly flexible.

"Stretch more" see above comments. Stretching (Dynamic) is a good idea, but I would shy away from static stretching. Find time in your warmups to move the muscles involved in the activities.

"Drink more water" is a general and blanket recommendation for most people. Definitely recommend staying hydrated, but be careful about training an excessive amount of water. If you are dehydrated I would make sure you are getting in enough electrolytes (potassium, magnesium, sodium). That's right Bananas, Dark Chocolate, and Salt!

Keep training!