there aren't any side effects to methotrexate?? Your doctor needs to read up on the literature! The most common side effects for methotrexate are stomach upset and fatigue and you've experience both. Taking a new medication can be a bit of a shock to the system and one of the ways I usually manage it is by starting at a fairly low dose and staying there until my body has gotten more used to it (as you've already experience from your second dose, your body does acclimatize to the new situation). Once that happens, I increase the dose gradually, waiting until my body acclimatize is at each increase. However, you have to weigh several factors carefully - methotrexate takes 6-8 weeks to really kick in, so if you're in a bad flare, you may want to keep increasing at the rate your doctor has suggested to make sure you get ahead of the disease. I recommend you call your doctor to explain the situation and ask their advice. . Given that he thinks there aren't any side effects with methotrexate, he may not be a lot of help, but you should make him aware that you are having side effects and would potentially like to ease into it a bit more.
If your doctor strongly recommends that you don't take a more gradual approach to getting to required dose, there are a number of things you can do to manage the side effects. One is to take your medication on e.g., a Friday evening so it doesn't interfere with your ability to work (assuming, of course, that you work Monday-Friday). This will enable you to get the rest you need for a couple of days. During times of stomach upset, eat bland foods - think anything white, steamed and not with a lot of flavor. Steamed or baked fish, toast, crackers, rice, bananas, etc. Fresh fruit and vegetables can also be easier to eat when you're nauseated. Stay away from fried and spicy foods. You may also want to check out my post on managing stomach side effects for more tips.
If not of this works, injectable methotrexate is generally a lot easier on the stomach, so that's an option to consider down the road.
Hang in there. It does get easier.