You should discontinue the hydrocortisone as it could have to do with a (lesser) side effect of hydrocortisone*.
The swelling and pain of your lower lip, could also be related to irritation or infection ( topical hydrocortisone is mildly immunosuppressive) and I think you should call your doctor's office tomorrow to report this
*For such an application, a class 6 or 7 mild hydrocortisone cream or ointment with moisturising effects is recommended.
Any different preparation in gel or lotion is not indicated because of the drying effects. Also because ot the high absorption rate in the lip and senstitivity, the lowest strength possible of the preparation should be prescribed.
Examples of mild preparations:
1. Class 6--> Fluocinolone acetonide cream 0.005%, triamcinolone
acetonide cream 0.02%, aclometaone dipropionate cream 0.05%, desonide cream 0.05%
2. Class 7--> Hydrocortisone acetate cream/ointment 1%
Applying aloe vera gel has worked for me and everyone I have recommended to for chapped lips and many other dermatological issues, however, check with your doctor tommorrow, if you could safely use it under the circumstances.
I would probably do it since I grew up with this, using it as a constitutional skin remedy, if I were you, but again, I cannot take any responsibilty, if you decide to try it.
Hope this helps, however, please note that my comments and suggestions are not intended as a substitute for medical advice.
I agree with TheLightSeeker that you should discontinue the hydrocortisone (immediately) as the swollen painful lip may be an allergic reaction to the cream. It is always worth trying out natural remedies and aloe vera is pretty good. Honey, Coconut oil, Almond oil, Jojoba oil and Olive oil can help too. Don't use petroleum jelly, this can help initially, but will dry the lips later.
Make sure that you drink plenty of water so as not to get dehydrated and don't lick your lips. Always protect your lips when going outside from the sun and wind.
Have you eaten or used any thing different? Just a thought. Sometimes though we can eat something that we may not know that we are allergic too or we can develop an allergy to something that we were OK with before. Keep a food diary to find out if there is any type of food (or even your toothpaste or cosmetics) that may be triggering off the lip swelling. You may need an antihistamine for the swelling.
Redness on the gums suggests that you have gum disease and the best way to treat this is by regularly brushing your teeth, in the morning and before going to bed as well as flossing regularly. If you do not know how to floss correctly, the dental hygienist will be able to show you. The gums are likely to bleed to begin with, but this will settle and the gums will start to improve. Healthy gums are a pink colour.
With regard to chapped and cracked lips, this can sometimes be from a fungal problem and for this you would need to use an antifungal cream specifically for use on the lips and mouth. Your doctor could take a swab to identify if there is any fungal problem to see if you would need to have an antifungal medication. The one that is used inside the mouth is Daktarin for oral use. There are also capsules that you take by mouth. As a home remedy natural live yogurt will help with regard to any fungal problems, you can eat this as well as apply it to the problem area.
The other reason for getting cracked and sore lips and especially in the corners of the mouth can be due to lacking in some vitamins and especially the Vitamin B group. Make sure you're getting plenty of Vitamins A, B, C, B2 (Riboflavin deficiency) and E to avoid cracked lips.
Eat a healthy and well balanced diet with lots of fresh fruit and vegetables. The vitamins mentioned above are in fortified breakfast cereals. You can find out more information with regard to vitamins and which foods contain which vitamin on the web.
Check out the website below that gives you more advice with regard to painful cracked lips, how to deal with them and the types of illnesses that can cause cracked lips.
Make an appointment to see your doctor again so that he can take a swab of the corners of your lips and from inside your mouth to find out if there is a fungal issue and also ask your doctor to run some blood tests with regard to ruling out any medical conditions. You should make your doctor aware of the swollen lips so that he can write that down on your medical records and that you may be allergic to one of the ingredients in the hydrocortisone cream. You may also need to consider seeing a dermatologist should things do not improve.
Let us know how you get on.